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.

Graph A

A curve in an x y plane, origin O.

Graph B

A curve in an x y plane, origin O.

Graph C

A curve in an x y plane, origin O.

Graph D

A curve in an x y plane, origin O.

Problem 2

Complete the table without graphing the equations. 

equation \(x \)-intercepts \(x \)-coordinate of the vertex

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.


    A curve in an x y plane, origin O.
  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.


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









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.

Graph 1

Parabola. Opens up. X intercepts = 0 and -7. 

Graph 2

Parabola. Opens up. Vertex = 0 comma -16. X intercepts = -4 and 4. 

Graph 3

Parabola. Opens up. X intercepts = -9 and 3. 


Problem 6

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

(From Unit 6, Lesson 8.)

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?

(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.)