Graphing Quadratic Equations

7.13.5 Graphing Quadratic Equations

7.13.5 • Graphing Quadratic Equations

Cool Down

1. Consider the quadratic equation $y = x^{2} - 4 x$ . Consider the graph of the equation when answering questions a and b.

a. Where are the $x$ -intercepts located?

Compare your answer:

The $x$ -intercepts are at $x = 0$ and $x = 4$ .

b. What is the $x$ -coordinate of the vertex?

2. The vertex is halfway between the intercepts at $x = 2$ .

2. Here is a graph of $y = x^{2}$ .

Graph of the parent quadratic function on the coordinate plane. The x-axis scale is 2 and extends from negative 8 to 8. The y-axis scale is 2 and extends from negative 8 to 12.

Sketch this graph on your own paper, then sketch a graph of $y = x^{2} + 5 x$ on the same graph. Briefly explain how you know where to sketch the second graph.

Compare your answer:

$x^{2} + 5 x$ is equivalent to $x (x + 5)$ , so the $x$ -intercepts are at $x = 0$ and $x = - 5$ . Calculate the vertex by finding the $x$ -coordinate in between $x = - 5$ and $x = 0$ which is $x = - 2.5$ . Substitute $x = - 2.5$ into the equation to find the $y$ -coordinate: $y = (- 2.5) 2 + 5 (- 2.5) = - 6.188$ . The vertex is at $(- 2.5, - 6.188)$ . The squared term has a positive coefficient so the graph opens upward. Adding a positive linear term to $x^{2}$ shifts the graph down and to the left.

Graph of the parent quadratic function on the coordinate plane and another function labeled as y equals x squared plus 5 times x. The x-axis scale is 2 and extends from negative 8 to 8. The y-axis scale is 2 and extends from negative 8 to 12.