# 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 \(y = x^2\).

- 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 \(y=x^2\).

### Problem 4

Select **all** equations whose graph opens upward.

\(y=\text-x^2 + 9x\)

\(y=10x-5x^2\)

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

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

\(y=x^2-8x-7\)

### 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.

### Problem 7

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?

### 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.