Q: Which of the following is the correct definition of a quadratic function?

$$f(x) = ax^2$ + bx + c$$, where $$a \neq 0$$

Q: Which of the following is the correct domain for the rational function $$f(x) = \frac{x+2}{x^2$-9}$$?

$$\{x \mid x \neq 3, x \neq -3\}$$

Question 1

Which of the following is the correct definition of a quadratic function?

Accepted Answer

$$f(x) = ax^2$ + bx + c$$, where $$a 
eq 0$$

Question 2

Given the quadratic function $$f(x) = -2(x-3)^2$ + 4$$, what is the vertex of the parabola?

Accepted Answer

$$(3, 4)$$

Question 3

A company models its revenue $$R (in $$dollars) as a function of price $$x by$$ $$R(x) = -5x^2$ + 100x. $$What price maximizes the revenue?

Accepted Answer

$$x = 10$$

Question 4

Which transformation is applied to the parent function $$f(x) = x^2$ to obtain g(x$$) = $$3(x+2)^2 - 5$?

Accepted Answer

Shift left 2 units, stretch vertically by 3, shift down 5 units

Question 5

For the quadratic function $$f(x) = 2x^2$ - 4x + 1$$, what is the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 6

A rectangular field is to be enclosed with 400 yards of fencing. What is the maximum area that can be enclosed?

Accepted Answer

$$10,000$$ square yards

Question 7

Given the polynomial $$f(x) = x^4$ - 2x^3$ + 5x - 7$$, what is the end behavior of the graph?

Accepted Answer

Rises to the left and rises to the right

Question 8

Which of the following statements about the zeros of a polynomial function is correct?

Accepted Answer

A zero of even multiplicity causes the graph to touch and turn around at the x-axis

Question 9

What is the horizontal asymptote of the rational function $$f(x) = \frac{3x^2$}{x^2$ - 1}$$?

Accepted Answer

$$y = 3$$

Question 10

For the rational function $$f(x) = \frac{x-2}{x^2$-1}$$, what are the vertical asymptotes?

Accepted Answer

$$x = 1$$ and $$x = -1$$

Question 11

Which of the following best describes the graph of $$f(x) = x^3$?

Accepted Answer

It is an odd function, symmetric with respect to the origin

Question 12

Given $$f(x) = \frac{2x^2$ - 3x + 1}{x-1}$$, what is the slant (oblique) asymptote?

Accepted Answer

$$y = 2x - 1$$

Question 13

If a polynomial $$f(x)$$ has degree 5, what is the maximum number of turning points its graph can have?

Accepted Answer

4

Question 14

Which of the following is the correct domain for the rational function $$f(x) = \frac{x+2}{x^2$-9}$$?

Accepted Answer

$$\{x \mid x 
eq 3, x 
eq -3\}$$

Question 15

A rain gutter is to be made from a 16-inch wide aluminum sheet by turning up the sides at an angle. What depth $$x$$ maximizes the cross-sectional area if the gutter is open at the top?

Accepted Answer

$$x = 4$$

Question 16

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

Accepted Answer

The graph touches and turns around at $$x = -1$$

Question 17

Which of the following is a possible set of rational zeros for $$f(x) = 2x^3$ - 3x^2$ + 4x - 5$$ according to the Rational Zero Theorem?

Accepted Answer

$$\pm1, \pm5, \pm\frac{1}{2}, \pm\frac{5}{2}$$

Question 18

If $$f(x) = x^2$ - 4x + 3$$, for which values of $$x is$$ $$f(x) \u003e 0$$?

Accepted Answer

$$(-\infty, 1) \cup (3, \infty)$$

Question 19

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

Accepted Answer

Falls to the left and rises to the right

Quadratic, Polynomial, and Rational Functions: Properties, Graphs, and Applications

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