Q: What is the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7 as$$ $$x \to \infty$$ and $$x \to -\infty$$?

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

Question 1

Which of the following is the correct vertex form of the quadratic function $$f(x) = x^2$ + 6x + 7$$?

Accepted Answer

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

Question 2

Given the quadratic function $$f(x) = -2(x + 1)^2$ + 2$$, what is the vertex and does it represent a minimum or maximum?

Accepted Answer

Vertex: $$(-1, 2)$$, Maximum

Question 3

Which of the following functions is NOT a polynomial function?

Accepted Answer

$$f(x) = 2x$$^{-1}$$ + 3x$$

Question 4

What is the end behavior of the polynomial $$f(x) = -3x^5$ + 2x^3$ - x + 7 as$$ $$x 	o \infty$$ and $$x 	o -\infty$$?

Accepted Answer

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

Question 5

For the polynomial $$f(x) = 2x(x-3)^2$(x+4)^3$$, what is the multiplicity of the zero at $$x = -4$ and does the graph cross or touch the x-axis at this point?

Accepted Answer

Multiplicity: 3, Crosses the x-axis

Question 6

What is the maximum number of turning points for the polynomial $$f(x) = 6x^4$ + 2x$$?

Accepted Answer

3

Question 7

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 19.6t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$21.6$$ meters

Question 8

Given $$f(x) = (3x + 2)(x - 1)^2$, what is the behavior of the graph at x = 1$?

Accepted Answer

Touches the x-axis and turns around

Question 9

Which of the following describes the end behavior of $$f(x) = 4x^6$ - 2x^3$ + 1$$?

Accepted Answer

Both ends rise to $$\infty$$

Question 10

If a polynomial function has degree $$n = 7$$, what is the maximum number of turning points it can have?

Accepted Answer

6

Question 11

Given the quadratic function $$f(x) = (x-1)^2$ - 4$$, what are the x-intercepts?

Accepted Answer

$$x = 1 \pm 2 = -1, 3$$

Question 12

Which of the following is the standard form of the polynomial $$f(x) = x(x-2)(x+3)$$?

Accepted Answer

$$f(x) = x^3$ + x^2$ - 6x$$

Question 13

A polynomial function $$f(x)$$ has a leading term $$-5x^4. $$What is the end behavior of $$f(x)$$?

Accepted Answer

Both ends fall to $$-\infty$$

Question 14

Which of the following is true about the domain of any polynomial function?

Accepted Answer

The domain is all real numbers, $$(-\infty, \infty)$$

Question 15

Given $$f(x) = x^3$ - 6x^2$ + 11x - 6$$, which of the following is NOT a zero of $$f(x)$$?

Accepted Answer

$$x = 0$$

Question 16

A company models its profit with $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and for how many units sold does it occur?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$ thousand units

Question 17

For the polynomial $$f(x) = x^2$(x-1)^3(x+2$$)$, what is the total number of real zeros (counting multiplicity)?

Accepted Answer

6

Question 18

Which transformation occurs when the quadratic function $$f(x) = x^2$ is changed to f(x$$) = $$3(x-2)^2 + 5$?

Accepted Answer

Vertical stretch by 3, right shift by 2 units, up shift by 5 units

Question 19

Given $$f(x) = x^4$ - 5x^2$ + 4$$, what are the x-intercepts?

Accepted Answer

$$x = -2, -1, 1, 2$$

Question 20

If $$f(x) = 3x^3$ + 12x^2$ + 12x$$, what is the y-intercept of the function?

Accepted Answer

$$0$$

Study Guide: Quadratic and Polynomial Functions in College Algebra

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