Question 1

Given the quadratic function $$f(x) = -6(x - 2)^2$ + 6$$, what is the range of $$f in $$interval notation?

Accepted Answer

$$( -\infty, 6 ]$$

Question 2

A baseball is hit straight up, and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 24.5t + 1. $$How long does it take for the baseball to reach its maximum height?

Accepted Answer

$$2.5$$ seconds

Question 3

Given $$f(x) = x^3$ + 4x^2$ - 4x - 16$$, what are the $$x-$$intercepts of $$f$$?

Accepted Answer

$$x = -4, -2, 2$$

Question 4

Rewrite $$f(x) = -x^2$ + 4x - 7 in $$vertex form and identify the vertex.

Accepted Answer

Vertex: $$(2, -3)$$

Question 5

For the polynomial $$f(x) = x(x + 2)^2$(x - 2)$$, what is the multiplicity of the zero at $$x = 0$$?

Accepted Answer

$$2$$

Question 6

Use the Rational Zeros Theorem to list all possible rational zeros for $$f(x) = 11x^4$ - 4x^2$ - x - 125.$$

Accepted Answer

$$\pm 1, \pm 5, \pm 25, \pm 125, \pm \frac{1}{11}, \pm \frac{5}{11}, \pm \frac{25}{11}, \pm \frac{125}{11}$$

Question 7

Given the polynomial $$f(x) = x^3$ + 10x^2$ + 32x + 32$$ and knowing that $$x = -4 is a $$zero of multiplicity $$2$$, what is the remaining zero?

Accepted Answer

$$x = -2$$

Question 8

Solve the equation $$x^3 - 125 = 0$ in the complex numbers.

Accepted Answer

$$5, \frac{5}{2} + \frac{5\sqrt{3}}{2}i, \frac{5}{2} - \frac{5\sqrt{3}}{2}i$$

Question 9

If the end behavior of a polynomial graph is such that as $$x 	o -\infty$$, $$y 	o \infty$$ and as $$x 	o \infty$$, $$y 	o -\infty$$, what can you conclude about the degree and leading coefficient?

Accepted Answer

Degree is odd, leading coefficient is negative

Question 10

A quadratic function $$f(x) = 7x^2$ + 14x - 8$$ has a minimum value. What is the minimum value?

Accepted Answer

$$-15$$

Question 11

Given $$f(x) = -x^2$ + 2x - 7$$, what is the $$y-$$intercept?

Accepted Answer

$$-7$$

Question 12

Use synthetic division to find the remainder when $$f(x) = x^5$ + 3x^2$ + x + 4 is $$divided by $$x - 2.$$

Accepted Answer

$$50$$

Question 13

Form a third-degree polynomial with real coefficients and leading coefficient $$1$$ such that $$-4 + i$$ and $$-6$$ are zeros.

Accepted Answer

$$x^3$$ + $$14x^2 + 65x + 102$

Question 14

Given $$f(x) = x^3$ - 6x^2$ - 11x - 5$$, use synthetic division to divide by $$x + 1$$ and write $$f(x) in $$the form $$(x + 1)q(x) + r. $$What is $$q(x)$$?

Accepted Answer

$$x^2 - 7x - 4$

Question 15

For the function $$f(x) = -x^2$ + 4x - 7$$, does the graph open up or down?

Accepted Answer

Opens down

Question 16

Given $$f(x) = x(x + 2)^2$(x - 2)$$, what is the $$y-$$intercept?

Accepted Answer

$$0$$

Question 17

If $$x = -2 is $$used in synthetic division for $$f(x) = 2x^3$ - 5x^2$ + 3x - 4$$, what is the remainder?

Accepted Answer

$$-46$$

Question 18

Given $$f(x) = -6(x - 2)^2$ + 6$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 19

For the polynomial $$f(x) = x^3$ + 4x^2$ - 4x - 16$$, what is the $$y-$$intercept?

Accepted Answer

$$-16$$

College Algebra: Quadratic and Polynomial Functions Review Guidance

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