Lesson 13

Graphing the Standard Form (Part 2)

View Student Lesson

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.
A:

Graph A

B:

Graph B

C:

Graph C

D:

Graph D

1:

\(y = x^2+x\)

2:

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

3:

\(y = x^2 -x\)

4:

\(y = x^2 + 3x\)

Solution

For access, consult one of our IM Certified Partners.

Problem 2

Complete the table without graphing the equations. 

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

Solution

For access, consult one of our IM Certified Partners.

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 \(y=x^2\).

Solution

For access, consult one of our IM Certified Partners.

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:

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

Solution

For access, consult one of our IM Certified Partners.

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. 

 

Solution

For access, consult one of our IM Certified Partners.

Problem 6

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

A:

\((x+3)(x+4)\)

B:

\((x+3)(x+7)\)

C:

\((3x+4)(x+3)\)

D:

\((x+7)(3x+1)\)

1:

\(x^2+10x+21\)

2:

\(3x^2+13x+12\)

3:

\(3x^2+22x+7\)

4:

\(x^2+7x+12\)

Solution

For access, consult one of our IM Certified Partners.

(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?

Solution

For access, consult one of our IM Certified Partners.

(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.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 5, Lesson 15.)