Lesson 13

Graphing the Standard Form (Part 2)

Let’s change some other parts of a quadratic expression and see how they affect the graph.

Here are four graphs. Match each graph with the quadratic equation that it represents.

Complete the table without graphing the equations.

equation	$x$ -intercepts	$x$ -coordinate of the vertex
$y=x^2+12x$
$y=x^2-3x$
$y=\text-x^2+16x$
$y=\text-x^2-24x$

Here is a graph that represents $y = x^2$ .

Describe what would happen to the graph if the original equation were changed to $y=x^2-6x$ . Predict the $x$ - and $y$ -intercepts of the graph and the quadrant where the vertex is located.
Sketch the graph of the equation $y=x^2 -6x$ on the same coordinate plane as $y=x^2$ .

Select all equations whose graph opens upward.

$y=\text-x^2 + 9x$

$y=10x-5x^2$

$y=(2x-1)^2$

$y=(1-x)(2+x)$

$y=x^2-8x-7$

Technology required. Write an equation for a function that can be represented by each given graph. Then, use graphing technology to check each equation you wrote.