Question 1

Which of the following statements is TRUE about the vertex of a parabola given by $$y = ax^2$ + bx + c$$?

Accepted Answer

The vertex is at the point $$\left( \frac{-b}{2a}, f\left(\frac{-b}{2a}\right) \right).$$

Question 2

Given the quadratic function $$y = -3x^2$ + 6x - 2$$, which statement is correct?

Accepted Answer

The parabola opens downward and the vertex is a maximum.

Question 3

What is the axis of symmetry for the quadratic function $$y = 2x^2$ - 8x + 5$$?

Accepted Answer

$$x = 2$$

Question 4

A company models its profit with $$P(x) = -x^2$ + 212x - 5500. $$How many units should be sold to maximize profit?

Accepted Answer

$$x = 106$$

Question 5

Which of the following is the vertex form of a quadratic equation?

Accepted Answer

$$y = a(x - h)^2$ + k$$

Question 6

If a parabola opens upward, which of the following must be true?

Accepted Answer

The leading coefficient $$a is $$positive.

Question 7

Given the function $$y = 2x^2$ - 12x + 16$$, what are the x-intercepts?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 8

Which of the following best describes the zeros of a quadratic function?

Accepted Answer

The points where the parabola crosses the x-axis.

Question 9

A quadratic function is given by $$y = a(x - 3)^2$ + 7. $$What is the vertex of this parabola?

Accepted Answer

$$(3, 7)$$

Question 10

If the graph of $$y = ax^2$ + bx + c is $$wider than the graph of $$y = x^2$, what can you conclude about $$|a|$$?

Accepted Answer

$$|a| \u003c 1$$

Question 11

A projectile is launched 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 projectile?

Accepted Answer

$$22$$ meters at $$t = 2$$ seconds

Question 12

Which of the following is NOT a characteristic of a quadratic function?

Accepted Answer

Its graph is always symmetric about the y-axis.

Question 13

Given the quadratic function $$y = -2x^2$ + 3x - 6$$, determine if the vertex is a maximum or minimum.

Accepted Answer

Maximum

Question 14

Which real-world scenario can be modeled by a quadratic function?

Accepted Answer

The profit of a company as a function of units sold, where profit increases then decreases.

Question 15

If $$y = 2(x - 1)^2$ - 2$$, what is the minimum value of $$y$$?

Accepted Answer

$$-2$$

Question 16

Which calculator feature would you use to fit a quadratic model to a set of data points?

Accepted Answer

QuadReg

Quadratic Functions: Graphs, Properties, and Applications

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