![\"Graph](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/11\/02170330\/CNX_Precalc_Figure_03_02_0022.jpg\")
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The [latex]y[\/latex]-intercept is the point at which the parabola crosses the [latex]y[\/latex]-axis. The [latex]x[\/latex]-intercepts are the points at which the parabola crosses the [latex]x[\/latex]-axis. If they exist, the [latex]x[\/latex]-intercepts represent the zeros<\/strong>, or roots<\/strong>, of the quadratic function, the values of [latex]x[\/latex] at which [latex]y=0[\/latex].<\/p>\n The places where a function's graph crosses the horizontal axis are the places where the function value equals zero. You've seen that these values are called horizontal intercepts<\/em>, [latex]x[\/latex]-intercepts<\/em>, and zeros<\/em> so far. They can also be referred to as the roots<\/em> of a function.<\/p>\n<\/section>\n Determine the vertex, axis of symmetry, zeros, and [latex]y[\/latex]-intercept of the parabola shown below.<\/p>\n [reveal-answer q=\"366804\"]Show Solution[\/reveal-answer]<\/p>\n [hidden-answer a=\"366804\"]<\/p>\n The vertex is the turning point of the graph. We can see that the vertex is at [latex](3,1)[\/latex]. The axis of symmetry is the vertical line that intersects the parabola at the vertex. So the axis of symmetry is [latex]x=3[\/latex]. This parabola does not cross the [latex]x[\/latex]-axis, so it has no zeros. It crosses the [latex]y[\/latex]-axis at [latex](0, 7)[\/latex] so this is the [latex]y[\/latex]-intercept.<\/p>\n [\/hidden-answer]<\/p>\n<\/section>\n The graph of a quadratic function is a U-shaped curve called a parabola<\/strong>. One important feature of the graph is that it has an extreme point, called the vertex<\/strong>. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value<\/strong> of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value<\/strong>. In either case, the vertex is a turning point on the graph. The graph is also symmetric with a vertical line drawn through the vertex, called the axis of symmetry<\/strong>.<\/p>\n <\/p>\n The [latex]y[\/latex]-intercept is the point at which the parabola crosses the [latex]y[\/latex]-axis. The [latex]x[\/latex]-intercepts are the points at which the parabola crosses the [latex]x[\/latex]-axis. If they exist, the [latex]x[\/latex]-intercepts represent the zeros<\/strong>, or roots<\/strong>, of the quadratic function, the values of [latex]x[\/latex] at which [latex]y=0[\/latex].<\/p>\n The places where a function’s graph crosses the horizontal axis are the places where the function value equals zero. You’ve seen that these values are called horizontal intercepts<\/em>, [latex]x[\/latex]-intercepts<\/em>, and zeros<\/em> so far. They can also be referred to as the roots<\/em> of a function.<\/p>\n<\/section>\n Determine the vertex, axis of symmetry, zeros, and [latex]y[\/latex]-intercept of the parabola shown below.<\/p>\n![\"Graph](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2016\/11\/02170333\/CNX_Precalc_Figure_03_02_0032.jpg\")
<\/center>\nKey Features of a Parabola’s Graph<\/h2>\n
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