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.

Problem 1

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

Problem 2

Complete the table without graphing the equations.

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

Problem 3

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

1. 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.

2. Sketch the graph of the equation $$y=x^2 -6x$$ on the same coordinate plane as $$y=x^2$$.

Problem 4

Select all equations whose graph opens upward.

A:

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

B:

$$y=10x-5x^2$$

C:

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

D:

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

E:

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

Problem 5

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.

Problem 6

Match each quadratic expression that is written as a product with an equivalent expression that is expanded.

(From Unit 6, Lesson 8.)

When buying a home, many mortgage companies require a down payment of 20% of the price of the house. What is the down payment on a $125,000 home? (From Unit 5, Lesson 14.) Problem 8 A bank loans$4,000 to a customer at a $$9\frac{1}{2}\%$$ annual interest rate.

Write an expression to represent how much the customer will owe, in dollars, after 5 years without payment.

(From Unit 5, Lesson 15.)