# Lesson 11

Graphing from the Factored Form

### Problem 1

Select all true statements about the graph that represents $$y=2x(x-11)$$.

A:

Its $$x$$-intercepts are at $$(\text-2,0)$$ and $$(11,0)$$.

B:

Its $$x$$-intercepts are at $$(0,0)$$ and $$(11,0)$$.

C:

Its $$x$$-intercepts are at $$(2,0)$$ and $$(\text-11,0)$$.

D:

It has only one $$x$$-intercept.

E:

The $$x$$-coordinate of its vertex is -4.5.

F:

The $$x$$-coordinate of its vertex is 11.

G:

The $$x$$-coordinate of its vertex is 4.5.

H:

The $$x$$-coordinate of its vertex is 5.5.

### Solution

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### Problem 2

Select all equations whose graphs have a vertex with $$x$$-coordinate 2.

A:

$$y=(x-2)(x-4)$$

B:

$$y=(x-2)(x+2)$$

C:

$$y=(x-1)(x-3)$$

D:

$$y=x(x+4)$$

E:

$$y=x(x-4)$$

### Solution

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### Problem 3

Determine the $$x$$-intercepts and the $$x$$-coordinate of the vertex of the graph that represents each equation.

equation $$x$$-intercepts $$x$$-coordinate of the vertex
$$y=x(x-2)$$
$$y=(x-4)(x+5)$$
$$y= \text-5x (3-x)$$

### Solution

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### Problem 4

Which one is the graph of the equation $$y=(x-3)(x+5)$$?

A:

Graph A

B:

Graph B

C:

Graph C

D:

Graph D

### Solution

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### Problem 5

1. What are the $$x$$-intercepts of the graph of $$y=(x-2)(x-4)$$?
2. Find the coordinates of another point on the graph. Show your reasoning.
3. Sketch a graph of the equation $$y = (x-2)(x-4)$$.

### Solution

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### Problem 6

A company sells calculators. If the price of the calculator in dollars is $$p$$, the company estimates that it will sell $$10,\!000-120p$$ calculators.

Write an expression that represents the revenue in dollars from selling calculators if a calculator is priced at $$p$$ dollars.

### Solution

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(From Unit 6, Lesson 7.)

### Problem 7

Is $$(s+t)^2$$ equivalent to $$s^2+2st+t^2$$? Explain or show your reasoning.

### Solution

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(From Unit 6, Lesson 8.)

### Problem 8

Tyler is shopping for a truck. He found two trucks that he likes. One truck sells for \$7,200. A slightly older truck sells for 15% less. How much does the older truck cost?

### Solution

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(From Unit 5, Lesson 14.)

### Problem 9

Here are graphs of two exponential functions, $$f$$ and $$g$$.

The function $$f$$ is given by $$f(x) = 100 \boldcdot 2^x$$ while $$g$$ is given by $$g(x) = a \boldcdot b^x$$.

Based on the graphs of the functions, what can you conclude about $$a$$ and $$b$$?

### Solution

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(From Unit 5, Lesson 13.)

### Problem 10

Suppose $$G$$ takes a student’s grade and gives a student’s name as the output. Explain why $$G$$ is not a function.

### Solution

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(From Unit 4, Lesson 2.)