{"id":1814,"date":"2024-06-10T19:37:48","date_gmt":"2024-06-10T19:37:48","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/?post_type=chapter&p=1814"},"modified":"2025-08-14T00:20:15","modified_gmt":"2025-08-14T00:20:15","slug":"introduction-to-quadratic-functions-and-parabolas-learn-it-3","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/collegealgebra\/chapter\/introduction-to-quadratic-functions-and-parabolas-learn-it-3\/","title":{"raw":"Introduction to Quadratic Functions and Parabolas: Learn It 3","rendered":"Introduction to Quadratic Functions and Parabolas: Learn It 3"},"content":{"raw":"

Key Features of a Parabola's Graph<\/h2>\r\nThe graph of a quadratic function is a U-shaped curve called a\u00a0parabola<\/strong>. One important feature of the graph is that it has an extreme point, called the\u00a0vertex<\/strong>. If the parabola opens up, the vertex represents the lowest point on the graph, or the\u00a0minimum value<\/strong>\u00a0of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the\u00a0maximum 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\u00a0axis of symmetry<\/strong>.\r\n\r\n
\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]\"Graph Graph of a parabola with key features labeled[\/caption]\r\n\r\n<\/center>
<\/center> \r\n\r\nThe [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]\u00a0at which [latex]y=0[\/latex].\r\n\r\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\u00a0horizontal intercepts<\/em>, [latex]x[\/latex]-intercepts<\/em>,\u00a0and\u00a0zeros<\/em> so far. They can also be referred to as the\u00a0roots<\/em> of a function.<\/section>
Determine the vertex, axis of symmetry, zeros, and [latex]y[\/latex]-intercept of the parabola shown below.
\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"487\"]\"Graph Graph of a parabola[\/caption]\r\n\r\n<\/center>[reveal-answer q=\"366804\"]Show Solution[\/reveal-answer][hidden-answer a=\"366804\"]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.\r\n\r\n[\/hidden-answer]\r\n\r\n<\/section>
[ohm2_question hide_question_numbers=1]13808[\/ohm2_question]<\/section>","rendered":"

Key Features of a Parabola’s Graph<\/h2>\n

The graph of a quadratic function is a U-shaped curve called a\u00a0parabola<\/strong>. One important feature of the graph is that it has an extreme point, called the\u00a0vertex<\/strong>. If the parabola opens up, the vertex represents the lowest point on the graph, or the\u00a0minimum value<\/strong>\u00a0of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the\u00a0maximum 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\u00a0axis of symmetry<\/strong>.<\/p>\n

\n
\"Graph
Graph of a parabola with key features labeled<\/figcaption><\/figure>\n<\/div>\n
<\/div>\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]\u00a0at 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\u00a0horizontal intercepts<\/em>, [latex]x[\/latex]-intercepts<\/em>,\u00a0and\u00a0zeros<\/em> so far. They can also be referred to as the\u00a0roots<\/em> of a function.<\/section>\n
Determine the vertex, axis of symmetry, zeros, and [latex]y[\/latex]-intercept of the parabola shown below.<\/p>\n
\n
\"Graph
Graph of a parabola<\/figcaption><\/figure>\n<\/div>\n