Question 1

Which of the following equations best matches the graph shown in the first image (a parabola opening upward with vertex at $$(-1, -2)$$)?

Accepted Answer

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

Question 2

Given the graph in the second image (a downward opening parabola with vertex at $$(-6, 37)$$), which function does it represent?

Accepted Answer

$$f(x) = -x^2$ + 12x + 1$$

Question 3

For the function $$f(x) = x^2$ + 10x$$, what are the vertex and axis of symmetry?

Accepted Answer

Vertex: $$(-5, -25)$$; Axis: $$x = -5$$

Question 4

For the function $$f(x) = -x^2$ + 12x + 1$$, what is the vertex and axis of symmetry?

Accepted Answer

Vertex: $$(6, 37)$$; Axis: $$x = 6$$

Question 5

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

Accepted Answer

Vertex: $$(2, -4)$$; Intercepts: $$(0, 0), (4, 0)$$

Question 6

For the function $$f(x) = x^2$ + 2x - 3$$, what is the vertex and what are the x-intercepts?

Accepted Answer

Vertex: $$(-1, -4)$$; Intercepts: $$(1, 0), (-3, 0), (0, -3)$$

Question 7

For the function $$f(x) = -x^2$ + 6x - 5$$, what is the vertex and what are the x-intercepts?

Accepted Answer

Vertex: $$(3, -4)$$; Intercepts: $$(5, 0), (1, 0), (0, 5)$$

Question 8

What is the domain and range of the function $$f(x) = x^2$ + 12x + 36$$?

Accepted Answer

Domain: all real numbers; Range: $$\{y|y \geq 0\}$$

Question 9

What is the domain and range of the function $$f(x) = -x^2$ - 4x - 3$$?

Accepted Answer

Domain: all real numbers; Range: $$\{y|y \leq 1\}$$

Question 10

For the function $$f(x) = -9x^2$ - 2x - 8$$, on which intervals is the function increasing and decreasing?

Accepted Answer

Increasing on $$(-\infty, -\frac{1}{9})$$; Decreasing on $$(-\frac{1}{9}, \infty)$$

Question 11

Given a quadratic function with vertex $$(-1, 4)$$ and y-intercept $$(0, 3)$$, which of the following is the correct equation?

Accepted Answer

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

Question 12

For the function $$f(x) = -x^2$ - 2x + 1$$, does it have a maximum or minimum value, and what is that value?

Accepted Answer

Maximum; $$-1$$

Question 13

For the function $$f(x) = -5x^2$ - 2x - 4$$, does it have a maximum or minimum value, and what is that value?

Accepted Answer

Maximum; $$\frac{19}{5}$$

Question 14

Are the functions $$f(x) = 9x - 7$$ and $$g(x) = \frac{x + 9}{7}$$ inverses of each other?

Accepted Answer

No

Question 15

Are the functions $$f(x) = 7x^2$ + 1$$ and $$g(x) = \sqrt{x - 1}/7$$ inverses of each other?

Accepted Answer

Yes; Exclude the interval $$(-\infty, 1)$$

Question 16

If $$f(x) = 5x^2$ + 3$$ for $$x \geq 0$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt{\frac{x - 3}{5}}$$

Question 17

If $$f(x) = (x - 6)^3$, what is the inverse function f$$^{-1}$$(x)$$?

Accepted Answer

$$f^{-1}(x$$) = \sqrt[3]{x} + 6$$

Question 18

Is $$f(x) = -20x^5$ + \frac{1}{9}x^4$ - 7 a $$polynomial function? If so, what is its degree?

Accepted Answer

Yes; degree 5

Question 19

Is $$f(x) = x$$^{4/3}$$ - x^2$ + 2 a $$polynomial function? If not, why?

Accepted Answer

No; $$x is $$raised to non-integer $$4/3$$ power

Vertex and Axis of Symmetry for Quadratic Functions

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