Algebra 2 - Ch. 5 Polynomial Graphs Review

What is the smallest possible degree of the function? ​

Answer explanation

It's one more than the number of turning points!

Which factors must be part of the function that is graphed?

• (x+8)

• (x+2)

• (x-4)

• (x + 4)

• (x-2)

In the above graph complete the following end behavior:

As x --> -∞, f(x) --> ​ ​​ (a)  

As x --> +∞, f(x) --> ​​ (b)  

Which function could match the graph?

Answer explanation

The graph has x-int of (-3, 0), (-2, 0) and (1, 0) so it must have factors of (x+3)(x+2)(x-1). It also must be an odd degree.

It also has the y-intercept of (0, -1), so

we must have

-1 = a(0+3)(0+2)(0-1)

a = 1/6

f(x) = (x+2)(x-3)²(x-4)

Which choice best describes the zeros?

• -2, 3 (multiplicity 2), 4

• -2 (multiplicity 2), 3, 4

• 2, -3 (multiplicity 2), -4

• 2 (multiplicity 2), -3, -4

Tags

CCSS.HSA.APR.B.3

State the interval(s) where the function is decreasing.

• (-2, -0.5) ∪ (1, ∞)

• (0, -5.063) ∪ (0, ∞)

• (-∞, 0) ∪ (-5.063, 0)

• (-∞, -2) ∪ (-0.5, 1)

• (-2, 0) ∪ (-0.5, -5.063)

Answer explanation

Use the intervals of x-values where the graph has a negative slope.

What is the local maximum value?

• Max of 4 when x = 1.

• Max of 4 when x = 0.

• Max of 1 when x = -3

• Max of 0 when x = -1.

On the interval (-4, 2) which best describes the function?

• Concave up

• Concave down

• Increasing

• Decreasing

Answer explanation

Remember to look between the x-values of -4 and 2.

What are the roots of the quadratic function?

• -4 and -2

• 4 and 2

• -4 and 2

• 4 and -2

Tags

CCSS.HSA.APR.B.3

CCSS.HSA.REI.B.4

Use the graph of 𝑓(𝑥) = 2𝑥⁴ − 3𝑥² + 2x + 1 to find the approximate solution(s) to f(x) = -2

• 0

• -1

• -1.5

• 2

• 0.5