Question 1

Which of the following is the standard form of a quadratic function?

Accepted Answer

$$f(x) = ax^2$ + bx + c$$

Question 2

Given the quadratic function $$f(x) = 2(x - 3)^2$ + 5$$, what are the coordinates of the vertex?

Accepted Answer

$$(3, 5)$$

Question 3

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

Accepted Answer

$$x = 2$$

Question 4

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

Question 5

Which of the following statements is true about the graph of $$f(x) = a(x - h)^2$ + k$$ when $$a \u003c 0$$?

Accepted Answer

The parabola opens downward and the vertex is a maximum point.

Question 6

If the quadratic function $$f(x) = 3x^2$ - 6x + 7 is $$graphed, what is the $$y-$$intercept?

Accepted Answer

$$7$$

Question 7

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

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 8

A company models its profit with $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What number of units sold maximizes the profit?

Accepted Answer

$$x = 2$$

Question 9

Which of the following best describes the effect of increasing the value of $$|a| in$$ $$f(x) = a(x - h)^2$ + k$$?

Accepted Answer

The parabola becomes narrower.

Question 10

Given the quadratic function $$f(x) = 2x^2$ + 8x + 5$$, what is the minimum value of the function?

Accepted Answer

$$-3$$

Question 11

If a parabola opens upward and its vertex is at $$(2, -3)$$, which of the following could be its equation?

Accepted Answer

$$f(x) = a(x - 2)^2$ - 3$$ with $$a \u003e 0$$

Question 12

Which of the following is the formula for the axis of symmetry of the quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$x = \frac{-b}{2a}$$

Question 13

A quadratic function has its vertex at $$(1, 4)$$ and passes through the point $$(3, 8). $$Which of the following is its equation?

Accepted Answer

Question 14

If $$f(x) = -2(x + 1)^2$ + 7$$, what is the maximum value of $$f(x)$$?

Accepted Answer

$$7$$

Question 15

Which of the following real-world scenarios can be modeled by a quadratic function?

Accepted Answer

The height of a projectile over time.

Question 16

Given $$f(x) = x^2$ + 6x + 8$$, what is the vertex of the parabola?

Accepted Answer

$$(-3, -1)$$

Question 17

If the graph of $$f(x) = a(x - h)^2$ + k is $$reflected over the $$x-$$axis, what happens to the value of $$a$$?

Accepted Answer

$$a$$ becomes $$-a$$

Question 18

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(2, -5). If$$ $$a = 1$$, what is the value of $$b$$?

Accepted Answer

$$-4$$

Question 19

Which of the following describes the minimum or maximum value of a quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

It occurs at $$x = \frac{-b}{2a}.$$

Question 20

If $$f(x) = 4(x - 1)^2$ - 9$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$-5$$

Quadratic Functions: Properties, Graphs, and Applications

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