Lesson 11

Finding Intersections

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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

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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

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Problem 3

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

Solution

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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

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(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

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(From Unit 2, Lesson 7.)

Problem 6

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

Solution

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(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

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(From Unit 2, Lesson 9.)