{"id":273,"date":"2026-01-30T23:00:13","date_gmt":"2026-01-30T23:00:13","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/polynomial-functions-get-stronger-key-precalculus-practice-page-answer-keys\/"},"modified":"2026-08-07T16:46:14","modified_gmt":"2026-08-07T16:46:14","slug":"polynomial-functions-get-stronger-key-precalculus-practice-page-answer-keys","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/chapter\/polynomial-functions-get-stronger-key-precalculus-practice-page-answer-keys\/","title":{"raw":"Polynomial Functions: Get Stronger Key -- Precalculus Practice Page Answer Keys","rendered":"Polynomial Functions: Get Stronger Key — Precalculus Practice Page Answer Keys"},"content":{"raw":"
\r\n

Quadratic Functions Solutions<\/h2>\r\n1.\u00a0If [latex]a=0[\/latex] then the function becomes a linear function.\r\n\r\n2.\u00a0If possible, we can use factoring. Otherwise, we can use the quadratic formula.\r\n\r\n3.\u00a0[latex]f\\left(x\\right)={\\left(x+1\\right)}^{2}-2[\/latex], Vertex [latex]\\left(-1,-4\\right)[\/latex]\r\n\r\n4.\u00a0[latex]f\\left(x\\right)=3{\\left(x - 1\\right)}^{2}-12[\/latex], Vertex [latex]\\left(1,-12\\right)[\/latex]\r\n\r\n5.\u00a0Minimum is [latex]-\\frac{17}{2}[\/latex] and occurs at [latex]\\frac{5}{2}[\/latex]. Axis of symmetry is [latex]x=\\frac{5}{2}[\/latex].\r\n\r\n6.\u00a0Minimum is [latex]-\\frac{17}{16}[\/latex] and occurs at [latex]-\\frac{1}{8}[\/latex]. Axis of symmetry is [latex]x=-\\frac{1}{8}[\/latex].\r\n\r\n7.\u00a0Domain is [latex]\\left(-\\infty ,\\infty \\right)[\/latex]. Range is [latex]\\left[2,\\infty \\right)[\/latex].\r\n\r\n8.\u00a0Domain is [latex]\\left(-\\infty ,\\infty \\right)[\/latex]. Range is [latex]\\left[-5,\\infty \\right)[\/latex].\r\n\r\n9.\u00a0[latex]\\left\\{3i\\sqrt{3},-3i\\sqrt{3}\\right\\}[\/latex]\r\n\r\n10.\u00a0[latex]\\left\\{2+i,2-i\\right\\}[\/latex]\r\n\r\n11.\u00a0[latex]\\left\\{5+i,5-i\\right\\}[\/latex]\r\n\r\n12.\u00a0[latex]\\left\\{-\\frac{1}{2}+\\frac{3}{2}i, -\\frac{1}{2}-\\frac{3}{2}i\\right\\}[\/latex]\r\n\r\n13.\u00a0[latex]\\left\\{-\\frac{3}{5}+\\frac{1}{5}i, -\\frac{3}{5}-\\frac{1}{5}i\\right\\}[\/latex]\r\n\r\n14.\u00a0Vertex [latex]\\left(1,\\text{ }-1\\right)[\/latex], Axis of symmetry is [latex]x=1[\/latex]. Intercepts are [latex]\\left(0,0\\right), \\left(2,0\\right)[\/latex].\r\n\r\n\"Graph\r\n\r\n15.\u00a0Vertex [latex]\\left(\\frac{5}{2},\\frac{-49}{4}\\right)[\/latex], Axis of symmetry is [latex]\\left(0,-6\\right),\\left(-1,0\\right),\\left(6,0\\right)[\/latex].\r\n\r\n\"Graph\r\n\r\n16.\u00a0Vertex [latex]\\left(\\frac{5}{4}, -\\frac{39}{8}\\right)[\/latex], Axis of symmetry is [latex]x=\\frac{5}{4}[\/latex]. Intercepts are [latex]\\left(0, -8\\right)[\/latex].\r\n\r\n\"Graph\r\n\r\n17.\u00a0[latex]f\\left(x\\right)={x}^{2}-4x+1[\/latex]\r\n\r\n18.\u00a0[latex]f\\left(x\\right)=-2{x}^{2}+8x - 1[\/latex]\r\n\r\n19.\u00a0[latex]f\\left(x\\right)=\\frac{1}{2}{x}^{2}-3x+\\frac{7}{2}[\/latex]\r\n\r\n20.\u00a0[latex]f\\left(x\\right)={x}^{2}+1[\/latex]\r\n\r\n21.\u00a0[latex]f\\left(x\\right)=2-{x}^{2}[\/latex]\r\n\r\n22.\u00a0[latex]f\\left(x\\right)=2{x}^{2}[\/latex]\r\n\r\n23.\u00a050 feet by 50 feet. Maximize [latex]f\\left(x\\right)=-{x}^{2}+100x[\/latex].\r\n\r\n24.\u00a02909.56 meters\r\n\r\n25.\u00a0$10.70\r\n

Polynomial Functions Solutions<\/h2>\r\n1.\u00a0The coefficient of the power function is the real number that is multiplied by the variable raised to a power. The degree is the highest power appearing in the function.\r\n\r\n2.\u00a0As x<\/em>\u00a0decreases without bound, so does [latex]f\\left(x\\right)[\/latex].\u00a0As x<\/em>\u00a0increases without bound, so does [latex]f\\left(x\\right)[\/latex].\r\n\r\n3.\u00a0Degree = 2, Coefficient = \u20132\r\n\r\n4.\u00a0Degree =4, Coefficient = \u20132\r\n\r\n5.\u00a0[latex]\\text{As }x\\to \\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to -\\infty ,f\\left(x\\right)\\to \\infty[\/latex]\r\n\r\n6.\u00a0[latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to -\\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to -\\infty[\/latex]\r\n\r\n7.\u00a0[latex]\\text{As }x\\to \\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to -\\infty ,f\\left(x\\right)\\to -\\infty[\/latex]\r\n\r\n8. y<\/em>-intercept is [latex]\\left(0,12\\right)[\/latex], t<\/em>-intercepts are [latex]\\left(1,0\\right);\\left(-2,0\\right);\\text{and }\\left(3,0\\right)[\/latex].\r\n\r\n9.\u00a0y<\/em>-intercept is [latex]\\left(0,-16\\right)[\/latex]. x<\/em>-intercepts are [latex]\\left(2,0\\right)[\/latex] and [latex]\\left(-2,0\\right)[\/latex].\r\n\r\n10.\u00a0y<\/em>-intercept is [latex]\\left(0,0\\right)[\/latex].i x-intercepts are [latex]\\left(0,0\\right),\\left(4,0\\right)[\/latex], and [latex]\\left(-2, 0\\right)[\/latex].\r\n\r\n11. 3\r\n\r\n12. 5\r\n\r\n13.\u00a0[latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to \\infty[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
x<\/em><\/th>\r\nf<\/em>(x<\/em>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
10<\/td>\r\n9,500<\/td>\r\n<\/tr>\r\n
100<\/td>\r\n99,950,000<\/td>\r\n<\/tr>\r\n
\u201310<\/td>\r\n9,500<\/td>\r\n<\/tr>\r\n
\u2013100<\/td>\r\n99,950,000<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n14.\u00a0[latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to -\\infty[\/latex]\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
x<\/em><\/th>\r\nf<\/em>(x<\/em>)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
10<\/td>\r\n\u2013504<\/td>\r\n<\/tr>\r\n
100<\/td>\r\n\u2013941,094<\/td>\r\n<\/tr>\r\n
\u201310<\/td>\r\n1,716<\/td>\r\n<\/tr>\r\n
\u2013100<\/td>\r\n1,061,106<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n15.\u00a0The y<\/em>-intercept is [latex]\\left(0, 0\\right)[\/latex].\u00a0The x<\/em>-intercepts are [latex]\\left(0, 0\\right),\\text{ }\\left(2, 0\\right)[\/latex]. [latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to \\infty[\/latex]\r\n\"Graph\r\n\r\n16.\u00a0The y<\/em>-intercept is [latex]\\left(0, -81\\right)[\/latex].\u00a0The x<\/em>-intercept are [latex]\\left(3, 0\\right),\\text{ }\\left(-3, 0\\right)[\/latex]. [latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to \\infty[\/latex]\r\n\"Graph\r\n\r\n17.\u00a0The y<\/em>-intercept is [latex]\\left(0, 0\\right)[\/latex]. The x<\/em>-intercepts are [latex]\\left(-3, 0\\right),\\text{ }\\left(0, 0\\right),\\text{ }\\left(5, 0\\right)[\/latex]. [latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to -\\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to \\infty[\/latex]\r\n\"Graph\r\n\r\n18.\u00a0[latex]f\\left(x\\right)={x}^{2}-4[\/latex]\r\n\r\n19.\u00a0[latex]f\\left(x\\right)={x}^{3}-4{x}^{2}+4x[\/latex]\r\n\r\n20.\u00a0[latex]f\\left(x\\right)={x}^{4}+1[\/latex]\r\n\r\n21.\u00a0[latex]V\\left(x\\right)=4{x}^{3}-32{x}^{2}+64x[\/latex]\r\n

Graphs of Polynomial Functions Solutions<\/h2>\r\n1.\u00a0The x-<\/em>intercept is where the graph of the function crosses the x<\/em>-axis, and the zero of the function is the input value for which [latex]f\\left(x\\right)=0[\/latex].\r\n\r\n2.\u00a0[latex]\\left(-2,0\\right),\\left(3,0\\right),\\left(-5,0\\right)[\/latex]\r\n\r\n3.\u00a0[latex]\\left(3,0\\right),\\left(-1,0\\right),\\left(0,0\\right)[\/latex]\r\n\r\n4.\u00a0[latex]\\left(0,0\\right),\\text{ }\\left(-5,0\\right),\\text{ }\\left(4,0\\right)[\/latex]\r\n\r\n5.\u00a0[latex]\\left(-2,0\\right),\\left(2,0\\right),\\left(\\frac{1}{2},0\\right)[\/latex]\r\n\r\n6.\u00a0[latex]\\left(1,0\\right),\\text{ }\\left(-1,0\\right)[\/latex]\r\n\r\n7.\u00a0[latex]\\left(0,0\\right),\\left(\\sqrt{3},0\\right),\\left(-\\sqrt{3},0\\right)[\/latex]\r\n\r\n8.\u00a0[latex]f\\left(2\\right)=-10[\/latex]\u00a0and [latex]f\\left(4\\right)=28[\/latex].\u00a0Sign change confirms.\r\n\r\n9.\u00a0[latex]f\\left(1\\right)=3[\/latex]\u00a0and [latex]f\\left(3\\right)=-77[\/latex].\u00a0Sign change confirms.\r\n\r\n10.\u00a00 with multiplicity 2, [latex]-\\frac{3}{2}[\/latex]\u00a0with multiplicity 5, 4 with multiplicity 2\r\n\r\n11.\u00a00 with multiplicity 2, \u20132 with multiplicity 2\r\n\r\n12.\u00a0[latex]\\text{0}\\text{ with multiplicity }4\\text{,}2\\text{ with multiplicity }1\\text{,}-\\text{1}\\text{ with multiplicity }1[\/latex]\r\n\r\n13.\u00a0[latex]\\frac{3}{2}[\/latex]\u00a0with multiplicity 2, 0 with multiplicity 3\r\n\r\n14.\u00a0x<\/em>-intercepts,\u00a0[latex]\\left(1, 0\\right)[\/latex]\u00a0with multiplicity 2, [latex]\\left(-4, 0\\right)[\/latex] with multiplicity 1, y-<\/em>intercept [latex]\\left(0, 4\\right)[\/latex]. As\u00a0[latex]x\\to -\\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to -\\infty[\/latex] , as\u00a0[latex]x\\to \\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to \\infty[\/latex] .\r\n\"Graph\r\n\r\n15.\u00a0x<\/em>-intercepts [latex]\\left(3,0\\right)[\/latex] with multiplicity 3, [latex]\\left(2,0\\right)[\/latex] with multiplicity 2, y<\/em>-intercept [latex]\\left(0,-108\\right)[\/latex] . As\u00a0[latex]x\\to -\\infty[\/latex],\u00a0[latex]f\\left(x\\right)\\to -\\infty[\/latex] , as [latex]x\\to \\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to \\infty[\/latex].\r\n\"Graph\r\n\r\n16.\u00a0x-intercepts [latex]\\left(0, 0\\right),\\left(-2, 0\\right),\\left(4, 0\\right)[\/latex]\u00a0with multiplicity 1, y<\/em>-intercept [latex]\\left(0, 0\\right)[\/latex]. As\u00a0[latex]x\\to -\\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to \\infty[\/latex] , as\u00a0[latex]x\\to \\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to -\\infty[\/latex].\r\n\"Graph\r\n\r\n17.\u00a0[latex]f\\left(x\\right)=-\\frac{2}{9}\\left(x - 3\\right)\\left(x+1\\right)\\left(x+3\\right)[\/latex]\r\n\r\n18. [latex]f\\left(x\\right)=-\\frac{1}{8}\\left(x +4\\right)\\left(x+2\\right)\\left(x-1\\right)\\left(x-3\\right)[\/latex]\r\n\r\n19. [latex]f\\left(x\\right)=\\frac{1}{12}\\left(x +2\\right)^2\\left(x+3\\right)^2[\/latex]\r\n\r\n20.\u00a0[latex]f\\left(x\\right)=\\frac{1}{3}{\\left(x - 3\\right)}^{2}{\\left(x - 1\\right)}^{2}\\left(x+3\\right)[\/latex]\r\n\r\n21.\u00a0[latex]f\\left(x\\right)=-2\\left(x+3\\right)\\left(x+2\\right)\\left(x - 1\\right)[\/latex]\r\n\r\n22. [latex]f\\left(x\\right)=-\\frac{3}{2}{\\left(2x - 1\\right)}^{2}\\left(x - 6\\right)\\left(x+2\\right)[\/latex]\r\n\r\n23.\u00a0[latex]f\\left(x\\right)=4{x}^{3}-36{x}^{2}+80x[\/latex]\r\n\r\n24.\u00a0[latex]f\\left(x\\right)=4{x}^{3}-36{x}^{2}+60x+100[\/latex]\r\n\r\n25.\u00a0[latex]f\\left(x\\right)=\\pi \\left(9{x}^{3}+45{x}^{2}+72x+36\\right)[\/latex]\r\n\r\n<\/div>","rendered":"
\n

Quadratic Functions Solutions<\/h2>\n

1.\u00a0If [latex]a=0[\/latex] then the function becomes a linear function.<\/p>\n

2.\u00a0If possible, we can use factoring. Otherwise, we can use the quadratic formula.<\/p>\n

3.\u00a0[latex]f\\left(x\\right)={\\left(x+1\\right)}^{2}-2[\/latex], Vertex [latex]\\left(-1,-4\\right)[\/latex]<\/p>\n

4.\u00a0[latex]f\\left(x\\right)=3{\\left(x - 1\\right)}^{2}-12[\/latex], Vertex [latex]\\left(1,-12\\right)[\/latex]<\/p>\n

5.\u00a0Minimum is [latex]-\\frac{17}{2}[\/latex] and occurs at [latex]\\frac{5}{2}[\/latex]. Axis of symmetry is [latex]x=\\frac{5}{2}[\/latex].<\/p>\n

6.\u00a0Minimum is [latex]-\\frac{17}{16}[\/latex] and occurs at [latex]-\\frac{1}{8}[\/latex]. Axis of symmetry is [latex]x=-\\frac{1}{8}[\/latex].<\/p>\n

7.\u00a0Domain is [latex]\\left(-\\infty ,\\infty \\right)[\/latex]. Range is [latex]\\left[2,\\infty \\right)[\/latex].<\/p>\n

8.\u00a0Domain is [latex]\\left(-\\infty ,\\infty \\right)[\/latex]. Range is [latex]\\left[-5,\\infty \\right)[\/latex].<\/p>\n

9.\u00a0[latex]\\left\\{3i\\sqrt{3},-3i\\sqrt{3}\\right\\}[\/latex]<\/p>\n

10.\u00a0[latex]\\left\\{2+i,2-i\\right\\}[\/latex]<\/p>\n

11.\u00a0[latex]\\left\\{5+i,5-i\\right\\}[\/latex]<\/p>\n

12.\u00a0[latex]\\left\\{-\\frac{1}{2}+\\frac{3}{2}i, -\\frac{1}{2}-\\frac{3}{2}i\\right\\}[\/latex]<\/p>\n

13.\u00a0[latex]\\left\\{-\\frac{3}{5}+\\frac{1}{5}i, -\\frac{3}{5}-\\frac{1}{5}i\\right\\}[\/latex]<\/p>\n

14.\u00a0Vertex [latex]\\left(1,\\text{ }-1\\right)[\/latex], Axis of symmetry is [latex]x=1[\/latex]. Intercepts are [latex]\\left(0,0\\right), \\left(2,0\\right)[\/latex].<\/p>\n

\"Graph<\/p>\n

15.\u00a0Vertex [latex]\\left(\\frac{5}{2},\\frac{-49}{4}\\right)[\/latex], Axis of symmetry is [latex]\\left(0,-6\\right),\\left(-1,0\\right),\\left(6,0\\right)[\/latex].<\/p>\n

\"Graph<\/p>\n

16.\u00a0Vertex [latex]\\left(\\frac{5}{4}, -\\frac{39}{8}\\right)[\/latex], Axis of symmetry is [latex]x=\\frac{5}{4}[\/latex]. Intercepts are [latex]\\left(0, -8\\right)[\/latex].<\/p>\n

\"Graph<\/p>\n

17.\u00a0[latex]f\\left(x\\right)={x}^{2}-4x+1[\/latex]<\/p>\n

18.\u00a0[latex]f\\left(x\\right)=-2{x}^{2}+8x - 1[\/latex]<\/p>\n

19.\u00a0[latex]f\\left(x\\right)=\\frac{1}{2}{x}^{2}-3x+\\frac{7}{2}[\/latex]<\/p>\n

20.\u00a0[latex]f\\left(x\\right)={x}^{2}+1[\/latex]<\/p>\n

21.\u00a0[latex]f\\left(x\\right)=2-{x}^{2}[\/latex]<\/p>\n

22.\u00a0[latex]f\\left(x\\right)=2{x}^{2}[\/latex]<\/p>\n

23.\u00a050 feet by 50 feet. Maximize [latex]f\\left(x\\right)=-{x}^{2}+100x[\/latex].<\/p>\n

24.\u00a02909.56 meters<\/p>\n

25.\u00a0$10.70<\/p>\n

Polynomial Functions Solutions<\/h2>\n

1.\u00a0The coefficient of the power function is the real number that is multiplied by the variable raised to a power. The degree is the highest power appearing in the function.<\/p>\n

2.\u00a0As x<\/em>\u00a0decreases without bound, so does [latex]f\\left(x\\right)[\/latex].\u00a0As x<\/em>\u00a0increases without bound, so does [latex]f\\left(x\\right)[\/latex].<\/p>\n

3.\u00a0Degree = 2, Coefficient = \u20132<\/p>\n

4.\u00a0Degree =4, Coefficient = \u20132<\/p>\n

5.\u00a0[latex]\\text{As }x\\to \\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to -\\infty ,f\\left(x\\right)\\to \\infty[\/latex]<\/p>\n

6.\u00a0[latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to -\\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to -\\infty[\/latex]<\/p>\n

7.\u00a0[latex]\\text{As }x\\to \\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to -\\infty ,f\\left(x\\right)\\to -\\infty[\/latex]<\/p>\n

8. y<\/em>-intercept is [latex]\\left(0,12\\right)[\/latex], t<\/em>-intercepts are [latex]\\left(1,0\\right);\\left(-2,0\\right);\\text{and }\\left(3,0\\right)[\/latex].<\/p>\n

9.\u00a0y<\/em>-intercept is [latex]\\left(0,-16\\right)[\/latex]. x<\/em>-intercepts are [latex]\\left(2,0\\right)[\/latex] and [latex]\\left(-2,0\\right)[\/latex].<\/p>\n

10.\u00a0y<\/em>-intercept is [latex]\\left(0,0\\right)[\/latex].i x-intercepts are [latex]\\left(0,0\\right),\\left(4,0\\right)[\/latex], and [latex]\\left(-2, 0\\right)[\/latex].<\/p>\n

11. 3<\/p>\n

12. 5<\/p>\n

13.\u00a0[latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to \\infty[\/latex]<\/p>\n\n\n\n\n\n\n\n\n
x<\/em><\/th>\nf<\/em>(x<\/em>)<\/th>\n<\/tr>\n<\/thead>\n
10<\/td>\n9,500<\/td>\n<\/tr>\n
100<\/td>\n99,950,000<\/td>\n<\/tr>\n
\u201310<\/td>\n9,500<\/td>\n<\/tr>\n
\u2013100<\/td>\n99,950,000<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

14.\u00a0[latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to -\\infty[\/latex]<\/p>\n\n\n\n\n\n\n\n\n
x<\/em><\/th>\nf<\/em>(x<\/em>)<\/th>\n<\/tr>\n<\/thead>\n
10<\/td>\n\u2013504<\/td>\n<\/tr>\n
100<\/td>\n\u2013941,094<\/td>\n<\/tr>\n
\u201310<\/td>\n1,716<\/td>\n<\/tr>\n
\u2013100<\/td>\n1,061,106<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

15.\u00a0The y<\/em>-intercept is [latex]\\left(0, 0\\right)[\/latex].\u00a0The x<\/em>-intercepts are [latex]\\left(0, 0\\right),\\text{ }\\left(2, 0\\right)[\/latex]. [latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to \\infty[\/latex]
\n\"Graph<\/p>\n

16.\u00a0The y<\/em>-intercept is [latex]\\left(0, -81\\right)[\/latex].\u00a0The x<\/em>-intercept are [latex]\\left(3, 0\\right),\\text{ }\\left(-3, 0\\right)[\/latex]. [latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to \\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to \\infty[\/latex]
\n\"Graph<\/p>\n

17.\u00a0The y<\/em>-intercept is [latex]\\left(0, 0\\right)[\/latex]. The x<\/em>-intercepts are [latex]\\left(-3, 0\\right),\\text{ }\\left(0, 0\\right),\\text{ }\\left(5, 0\\right)[\/latex]. [latex]\\text{As }x\\to -\\infty ,f\\left(x\\right)\\to -\\infty ,\\text{ as }x\\to \\infty ,f\\left(x\\right)\\to \\infty[\/latex]
\n\"Graph<\/p>\n

18.\u00a0[latex]f\\left(x\\right)={x}^{2}-4[\/latex]<\/p>\n

19.\u00a0[latex]f\\left(x\\right)={x}^{3}-4{x}^{2}+4x[\/latex]<\/p>\n

20.\u00a0[latex]f\\left(x\\right)={x}^{4}+1[\/latex]<\/p>\n

21.\u00a0[latex]V\\left(x\\right)=4{x}^{3}-32{x}^{2}+64x[\/latex]<\/p>\n

Graphs of Polynomial Functions Solutions<\/h2>\n

1.\u00a0The x-<\/em>intercept is where the graph of the function crosses the x<\/em>-axis, and the zero of the function is the input value for which [latex]f\\left(x\\right)=0[\/latex].<\/p>\n

2.\u00a0[latex]\\left(-2,0\\right),\\left(3,0\\right),\\left(-5,0\\right)[\/latex]<\/p>\n

3.\u00a0[latex]\\left(3,0\\right),\\left(-1,0\\right),\\left(0,0\\right)[\/latex]<\/p>\n

4.\u00a0[latex]\\left(0,0\\right),\\text{ }\\left(-5,0\\right),\\text{ }\\left(4,0\\right)[\/latex]<\/p>\n

5.\u00a0[latex]\\left(-2,0\\right),\\left(2,0\\right),\\left(\\frac{1}{2},0\\right)[\/latex]<\/p>\n

6.\u00a0[latex]\\left(1,0\\right),\\text{ }\\left(-1,0\\right)[\/latex]<\/p>\n

7.\u00a0[latex]\\left(0,0\\right),\\left(\\sqrt{3},0\\right),\\left(-\\sqrt{3},0\\right)[\/latex]<\/p>\n

8.\u00a0[latex]f\\left(2\\right)=-10[\/latex]\u00a0and [latex]f\\left(4\\right)=28[\/latex].\u00a0Sign change confirms.<\/p>\n

9.\u00a0[latex]f\\left(1\\right)=3[\/latex]\u00a0and [latex]f\\left(3\\right)=-77[\/latex].\u00a0Sign change confirms.<\/p>\n

10.\u00a00 with multiplicity 2, [latex]-\\frac{3}{2}[\/latex]\u00a0with multiplicity 5, 4 with multiplicity 2<\/p>\n

11.\u00a00 with multiplicity 2, \u20132 with multiplicity 2<\/p>\n

12.\u00a0[latex]\\text{0}\\text{ with multiplicity }4\\text{,}2\\text{ with multiplicity }1\\text{,}-\\text{1}\\text{ with multiplicity }1[\/latex]<\/p>\n

13.\u00a0[latex]\\frac{3}{2}[\/latex]\u00a0with multiplicity 2, 0 with multiplicity 3<\/p>\n

14.\u00a0x<\/em>-intercepts,\u00a0[latex]\\left(1, 0\\right)[\/latex]\u00a0with multiplicity 2, [latex]\\left(-4, 0\\right)[\/latex] with multiplicity 1, y-<\/em>intercept [latex]\\left(0, 4\\right)[\/latex]. As\u00a0[latex]x\\to -\\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to -\\infty[\/latex] , as\u00a0[latex]x\\to \\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to \\infty[\/latex] .
\n\"Graph<\/p>\n

15.\u00a0x<\/em>-intercepts [latex]\\left(3,0\\right)[\/latex] with multiplicity 3, [latex]\\left(2,0\\right)[\/latex] with multiplicity 2, y<\/em>-intercept [latex]\\left(0,-108\\right)[\/latex] . As\u00a0[latex]x\\to -\\infty[\/latex],\u00a0[latex]f\\left(x\\right)\\to -\\infty[\/latex] , as [latex]x\\to \\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to \\infty[\/latex].
\n\"Graph<\/p>\n

16.\u00a0x-intercepts [latex]\\left(0, 0\\right),\\left(-2, 0\\right),\\left(4, 0\\right)[\/latex]\u00a0with multiplicity 1, y<\/em>-intercept [latex]\\left(0, 0\\right)[\/latex]. As\u00a0[latex]x\\to -\\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to \\infty[\/latex] , as\u00a0[latex]x\\to \\infty[\/latex] ,\u00a0[latex]f\\left(x\\right)\\to -\\infty[\/latex].
\n\"Graph<\/p>\n

17.\u00a0[latex]f\\left(x\\right)=-\\frac{2}{9}\\left(x - 3\\right)\\left(x+1\\right)\\left(x+3\\right)[\/latex]<\/p>\n

18. [latex]f\\left(x\\right)=-\\frac{1}{8}\\left(x +4\\right)\\left(x+2\\right)\\left(x-1\\right)\\left(x-3\\right)[\/latex]<\/p>\n

19. [latex]f\\left(x\\right)=\\frac{1}{12}\\left(x +2\\right)^2\\left(x+3\\right)^2[\/latex]<\/p>\n

20.\u00a0[latex]f\\left(x\\right)=\\frac{1}{3}{\\left(x - 3\\right)}^{2}{\\left(x - 1\\right)}^{2}\\left(x+3\\right)[\/latex]<\/p>\n

21.\u00a0[latex]f\\left(x\\right)=-2\\left(x+3\\right)\\left(x+2\\right)\\left(x - 1\\right)[\/latex]<\/p>\n

22. [latex]f\\left(x\\right)=-\\frac{3}{2}{\\left(2x - 1\\right)}^{2}\\left(x - 6\\right)\\left(x+2\\right)[\/latex]<\/p>\n

23.\u00a0[latex]f\\left(x\\right)=4{x}^{3}-36{x}^{2}+80x[\/latex]<\/p>\n

24.\u00a0[latex]f\\left(x\\right)=4{x}^{3}-36{x}^{2}+60x+100[\/latex]<\/p>\n

25.\u00a0[latex]f\\left(x\\right)=\\pi \\left(9{x}^{3}+45{x}^{2}+72x+36\\right)[\/latex]<\/p>\n<\/div>\n","protected":false},"author":13,"menu_order":4,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":224,"module-header":"- Select Header -","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/273"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/users\/13"}],"version-history":[{"count":3,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/273\/revisions"}],"predecessor-version":[{"id":393,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/273\/revisions\/393"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/parts\/224"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapters\/273\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/media?parent=273"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/pressbooks\/v2\/chapter-type?post=273"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/contributor?post=273"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/qrpracticepages\/wp-json\/wp\/v2\/license?post=273"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}