Question 1

Given the quadratic function $$h(t) = -16t^2$ + 80t + 96$$ representing the height of a baseball thrown upward, what does the constant 96 represent?

Accepted Answer

The initial height of the baseball, or the y-intercept

Question 2

For the function $$f(x) = ax^2$ + bx + c$$, if $$a \u003c 0$$, what can you conclude about the graph of the function?

Accepted Answer

The parabola opens downward

Question 3

Given the graph in Image 1, what is the factored form of the quadratic function?

Accepted Answer

$$y = a(x + 3)(x - 4)$$

Question 4

Given the graph in Image 2, what is the standard form of the quadratic function if the y-intercept is $$-12$$?

Accepted Answer

$$y = -x^2$ + 7x - 12$$

Question 5

For the function $$y = a(x - r)(x - s)$$, what do $$r$$ and $$s$$ represent?

Accepted Answer

The zeros (x-intercepts) of the function

Question 6

Given the vertex form $$y = a(x - h)^2$ + k$$, what does the point $$(h, k)$$ represent?

Accepted Answer

The vertex of the parabola

Question 7

A company charges $$x$$ dollars per item and can sell $$2000 - 4x$$ items. Each item costs $$6$$ dollars to produce. What is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = -4x^2$ + 1976x - 12000$$

Question 8

Given the graph in Image 3, what is the vertex form of the quadratic function?

Accepted Answer

$$y = a(x - 1)^2$ - 6$$

Question 9

If a quadratic function has a leading coefficient $$a \u003e 0$$, what can you say about its vertex?

Accepted Answer

The vertex is the minimum point of the parabola

Question 10

For the function $$h(t) = -16(t - 6)(t + 1)$$, what are the practical interpretations of the factors $$(t - 6)$$ and $$(t + 1)$$?

Accepted Answer

They represent the times when the baseball is at ground level (height zero)

Question 11

Given $$f(x) = -3x(2x - 7)$$, what is the standard form of the function?

Accepted Answer

$$f(x) = -6x^2$ + 21x$$

Question 12

If the vertex of a parabola is at $$(2.5, 196)$$ and the leading coefficient is negative, what does this tell you about the function?

Accepted Answer

The function has a maximum value at $$x = 2.5$$

Question 13

Which of the following best describes the effect of the sign of $$a in $$the quadratic function $$y = ax^2$ + bx + c$$?

Accepted Answer

If $$a \u003e 0$$, the parabola opens upward; if $$a \u003c 0$$, it opens downward

Question 14

Given the quadratic function $$y = 2(x - 1)^2$ - 6$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -6)$$

Question 15

If a quadratic function in standard form $$y = ax^2$ + bx + c$$ has $$c = 0$$, what does this mean for the graph?

Accepted Answer

The graph passes through the origin

Question 16

A company wants to maximize its profit, given by $$P(x) = -4x^2$ + 1976x - 12000. $$What price $$x$$ should the company charge to maximize profit?

Accepted Answer

$$x = 247$$

Quadratic Functions: Forms, Properties, and Applications

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