# Lesson 11

Finding Intersections

### Problem 1

What are the points of intersection between the graphs of the functions $$f(x)=x^2(x+1)$$ and $$g(x)=x+1$$?

### Problem 2

Select all the points of intersection between the graphs of the functions $$f(x)=(x+5)(x-2)$$ and $$g(x)=(2x+1)(x-2)$$.

A:

$$(\text-5, 0)$$

B:

$$(\text-\frac12, 0)$$

C:

$$(\text-2,\text-12)$$

D:

$$(2, 0)$$

E:

$$(4, 18)$$

F:

$$(5, 30)$$

### Problem 3

What are the solutions to the equation $$(x-3)(x+5)=\text-15$$?

### Problem 4

What are the $$x$$-intercepts of the graph of $$y=(5x+7)(2x-1)(x-4)$$?

A:

$$\text-\frac75, \text{-}\frac12, 4$$

B:

$$\frac57, \frac12, 4$$

C:

$$\text{-}\frac75, \frac12, 4$$

D:

$$\frac57, 2, 4$$

### Solution

(From Unit 2, Lesson 5.)

### Problem 5

Which polynomial function’s graph is shown here?

A:

$$f(x)=(x+1)(x+2)(x+4)$$

B:

$$f(x)=(x+1)(x-2)(x+4)$$

C:

$$f(x)=(x-1)(x+2)(x-4)$$

D:

$$f(x)=(x-1)(x-2)(x-4)$$

### Solution

(From Unit 2, Lesson 7.)

### Problem 6

Draw a rough sketch of the graph of $$g(x)=\text-x^2(x+2)$$.

### Solution

(From Unit 2, Lesson 10.)

### Problem 7

The graph of a polynomial function $$f$$ is shown.