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 \(g(x)=x+1\)?

Solution

For access, consult one of our IM Certified Partners.

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:

\((5, 30)\)

Solution

For access, consult one of our IM Certified Partners.

Problem 3

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

Solution

For access, consult one of our IM Certified Partners.

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

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 5.)

Problem 5

Which polynomial function’s graph is shown here?

polynomial function with roots of -2, 1, and 4
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

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 7.)

Problem 6

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

Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 10.)

Problem 7

The graph of a polynomial function \(f\) is shown.

graph of a polynomial function. x intercepts = -2, -1, 1, 2. y intercept = -4. the value of f of x decreases when x increases both in the positive and negative directions
  1. Is the degree of the polynomial odd or even? Explain how you know.
  2. What is the constant term of the polynomial?

Solution

For access, consult one of our IM Certified Partners.

(From Unit 2, Lesson 9.)