# 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.

### 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. $$y = \text-x^2 + 5$$

### 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.
(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.

(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.)