Q: Which of the following best describes the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Q: If $$f(x) = -2(x+4)(x-1)^3$, what is the end behavior of f(x$$)$$?

As $$x \to \infty$$, $$f(x) \to -\infty$$; as $$x \to -\infty$$, $$f(x) \to \infty$$

Question 1

Given the quadratic function $$f(x) = 2x^2$ - 8x + 6$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, -2)$$

Question 2

Which of the following best describes the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 3

A company models its daily profit with $$P(x) = -x^2$ + 10x - 16$$, where $$x is $$the number of items sold. What is the maximum profit, and how many items should be sold to achieve it?

Accepted Answer

Maximum profit is $$9 at$$ $$x = 5$$

Question 4

Which statement about the graph of $$f(x) = (x-1)^2$(x+2) is $$correct?

Accepted Answer

The graph touches the $$x-$$axis at $$x=1$$ and crosses at $$x=-2$$

Question 5

What is the $$y-$$intercept of the polynomial $$f(x) = 2(x-3)^2$(x+1)$$?

Accepted Answer

$$f(0) = 18$$

Question 6

How many turning points can the graph of a degree $$6$$ polynomial have at most?

Accepted Answer

$$5$$

Question 7

Solve the inequality $$(x-2)^2(x+1$$) \u003e 0$$. Which intervals are part of the solution?

Accepted Answer

$$(-\infty, -1) \cup (2, \infty)$$

Question 8

Given $$f(x) = x^2$ - 6x + 8$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 9

A polynomial $$f(x)$$ has a zero at $$x=3$$ with multiplicity $$4. $$What does the graph do at $$x=3$$?

Accepted Answer

Touches the $$x-$$axis and turns around

Question 10

Which of the following is the vertex form of the quadratic $$f(x) = x^2$ + 4x + 5$$?

Accepted Answer

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

Question 11

If $$f(x) = -2(x+4)(x-1)^3$, what is the end behavior of f(x$$)$$?

Accepted Answer

As $$x 	o \infty$$, $$f(x) 	o -\infty$$; as $$x 	o -\infty$$, $$f(x) 	o \infty$$

Question 12

Which of the following polynomials has $$x-$$intercepts at $$x = -2 ($$multiplicity $$2) $$and $$x = 3 ($$multiplicity $$1$$)?

Accepted Answer

$$f(x) = (x+2)^2$(x-3)$$

Question 13

A ball is thrown and its height in meters after $$t$$ seconds is $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 14

Which of the following describes the solution set for the inequality $$(x-1)^2(x+2$$) \leq 0$$?

Accepted Answer

$$[-2, 1]$$

Question 15

If a polynomial $$f(x)$$ has degree $$7$$, what is the maximum number of real zeros it can have?

Accepted Answer

$$7$$

Question 16

Given $$f(x) = 3x^2$ - 18x + 24$$, what is the local minimum value of $$f(x)$$?

Accepted Answer

$$-3$$

Question 17

Which of the following is true about the graph of $$f(x) = (x-2)^3$(x+1)^2$?

Accepted Answer

The graph crosses the $$x-$$axis at $$x=2$$ and touches at $$x=-1$$

Question 18

A polynomial $$f(x)$$ has the following zeros: $$x = -3 ($$multiplicity $$2$$), $$x = 1 ($$multiplicity $$3). $$What is the minimum degree of $$f(x)$$?

Accepted Answer

$$5$$

Question 19

Which of the following is the correct process to solve the polynomial inequality $$(x-4)^2(x+2$$) \geq 0$$?

Accepted Answer

Find $$x-$$intercepts, determine cross/touch, test intervals, and match intervals with the inequality

Quadratic and Polynomial Functions: Graphs, Properties, and Inequalities

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