Lesson 11

Finding Intersections

The practice problem answers are available at one of our IM Certified Partners

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:

$\frac57, 2, 4$

(From Algebra2, 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:

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

(From Algebra2, Unit 2, Lesson 7.)

Problem 6

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

(From Algebra2, 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?
(From Algebra2, Unit 2, Lesson 9.)