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 $$f(x) = -x^2$ + 4x - 7$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, -3)$$

Question 4

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

Accepted Answer

$$-4, -2, 2$$

Question 5

Which of the following is the correct axis of symmetry for the quadratic function $$f(x) = -x^2$ + 4x - 7$$?

Accepted Answer

$$x = 2$$

Question 6

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 7

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 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

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

Accepted Answer

$$-16$$

Question 10

A polynomial $$f(x) = x^3$ + 14x^2$ + 65x + 102$$ has zeros at $$-4 + i$$ and $$-6. $$What is the third zero?

Accepted Answer

$$-4 - i$$

Question 11

For the quadratic function $$f(x) = 7x^2$ + 14x - 8$$, does the function have a maximum or minimum value, and what is that value?

Accepted Answer

Minimum, $$-15$$

Question 12

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

Accepted Answer

2

Question 13

If the end behavior of a polynomial graph is 'down' on the left and 'up' on the right, what can you conclude about the degree and leading coefficient?

Accepted Answer

Degree is odd, leading coefficient is positive

Question 14

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 15

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

Accepted Answer

$$-7$$

Question 16

Which of the following is the correct vertex form for $$f(x) = -x^2$ + 4x - 7$$?

Accepted Answer

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

Question 17

If $$f(x) = x^3$ + 4x^2$ - 4x - 16$$, which of the following is the completely factored form?

Accepted Answer

$$(x + 2)(x - 2)(x + 4)$$

Question 18

A real-world scenario: A chemical reaction's temperature $$T (in$$ °C) over time $$t (in $$minutes) is modeled by $$T(t) = -2t^2$ + 8t + 10. $$What is the maximum temperature reached, and at what time does it occur?

Accepted Answer

Maximum temperature is $$18$$°C at $$t = 2$$ minutes

College Algebra Chapter 4 Review: Quadratic and Polynomial Functions

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