Lesson 12

Graphing the Standard Form (Part 1)

  • Let’s see how the numbers in expressions like \text-3x^2+4 affect their graph.

Problem 1

Here are four graphs. Match each graph with a 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

2:

y = x^2 + 5

3:

y = x^2 +7

4:

y = x^2 - 3

Problem 2

The two equations y=(x+2)(x+3) and y=x^2 + 5x + 6 are equivalent.

  1. Which equation helps find the x-intercepts most efficiently?
  2. Which equation helps find the y-intercept most efficiently?

Problem 3

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

On the same coordinate plane, sketch and label the graph that represents each equation:

  1. y = x^2 -4
  2. y = \text-x^2 + 5
A curve in an x y plane, origin O.

Problem 4

Select all equations whose graphs have a y-intercept with a positive y-coordinate.

A:

y=x^2 + 3x - 2

B:

y=x^2 - 10x

C:

y=(x-1)^2

D:

y=5x^2-3x-5

E:

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

Problem 5

  1. Describe how the graph of A(x)=|x| has to be shifted to match the given graph.
  2. Write an equation for the function represented by the graph.
Absolute value function with vertex at 2 comma 3.
(From Unit 4, Lesson 14.)

Problem 6

Here is a graph of the function g given by g(x) = a \boldcdot b^x.

What can you say about the value of b? Explain how you know. 

Graph of a decreasing exponential function g, x y plane, origin O.
(From Unit 5, Lesson 13.)

Problem 7

  1. What are the x-intercepts of the graph that represents y = (x+1)(x+5)? Explain how you know.
  2. What is the x-coordinate of the vertex of the graph that represents y = (x+1)(x+5)? Explain how you know.
  3. Find the y-coordinate of the vertex. Show your reasoning.
  4. Sketch a graph of y = (x+1)(x+5).
(From Unit 6, Lesson 11.)

Problem 8

Determine the x-intercepts, the vertex, and the y-intercept of the graph of each equation.

equation x-intercepts vertex y-intercept
y=(x-5)(x-3)      
y=2x(8-x)      
(From Unit 6, Lesson 11.)

Problem 9

Equal amounts of money were invested in stock A and stock B. In the first year, stock A increased in value by 20%, and stock B decreased by 20%. In the second year, stock A decreased in value by 20%, and stock B increased by 20%.

Was one stock a better investment than the other? Explain your reasoning.

(From Unit 5, Lesson 15.)