Question 1

Given the quadratic function $$f(x) = 2x^2$ - 8x + 3$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, -5)$$

Question 2

A ball is thrown upward from the ground with an initial velocity such that its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t. $$What is the maximum height reached by the ball?

Accepted Answer

$$25$$ meters

Question 3

Which of the following is the correct formula to find the $$x-$$coordinate of the vertex of a parabola given by $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

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

Question 4

A company models its profit $$P(x) in $$thousands of dollars by the function $$P(x) = -3x^2$ + 12x + 5$$, where $$x is $$the number of units sold (in thousands). How many units should be sold to maximize profit?

Accepted Answer

$$x = 2$$

Question 5

If the quadratic function $$f(x) = x^2$ - 6x + 8 is $$rewritten in vertex form, what is the vertex?

Accepted Answer

$$(3, -1)$$

Question 6

A satellite dish is shaped like a parabola. Its cross-section can be modeled by $$y = 0.5x^2$ - 4x + 7. $$What is the minimum value of $$y$$?

Accepted Answer

$$3$$

Question 7

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

Accepted Answer

$$x = 2$$

Question 8

A projectile is launched and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 14.7t + 2. $$After how many seconds does it reach its maximum height?

Accepted Answer

$$t = 1.5$$

Question 9

Which of the following statements is true about the graph of $$f(x) = ax^2$ + bx + c if$$ $$a \u003e 0$$?

Accepted Answer

The parabola opens upward and has a minimum point.

Question 10

A rectangular garden is to be fenced on three sides with 60 meters of fencing, with one side against a wall. What is the maximum area that can be enclosed?

Accepted Answer

$$300$$ square meters

Question 11

If $$f(x) = 3x^2$ - 12x + 7$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-5$$

Question 12

A quadratic function models the path of a diver: $$h(x) = -2x^2$ + 8x + 3$$, where $$h is $$the height in meters and $$x is $$the horizontal distance in meters. What is the maximum height the diver reaches?

Accepted Answer

$$11$$ meters

Question 13

Which of the following is the correct vertex form of the quadratic $$f(x) = x^2$ + 6x + 5$$?

Accepted Answer

$$f(x) = (x + 3)^2$ - 4$$

Question 14

A farmer wants to build a rectangular pen against a barn using 80 meters of fencing for the other three sides. What is the maximum area the pen can have?

Accepted Answer

$$800$$ square meters

Question 15

Given the quadratic function $$f(x) = -2x^2$ + 4x + 6$$, what is the $$y-$$coordinate of the vertex?

Accepted Answer

$$10$$

Question 16

If the vertex of a parabola is at $$(h, k)$$ and the equation is $$f(x) = a(x - h)^2$ + k$$, which value represents the minimum or maximum value of the function?

Accepted Answer

$$k$$

Question 17

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(1, -4). If$$ $$a = 2$$ and $$b = -4$$, what is the value of $$c$$?

Accepted Answer

$$-2$$

Question 18

A bridge is designed in the shape of a parabola with its vertex at the highest point. If the equation is $$y = -0.25x^2$ + 6$$, what is the height of the bridge at its vertex?

Accepted Answer

$$6$$ meters

Question 19

Which of the following best describes the effect of increasing the value of $$a in$$ $$f(x) = a(x - h)^2$ + k ($$with $$a \u003e 0) on $$the graph of the parabola?

Accepted Answer

The parabola becomes narrower.

Question 20

A quadratic function $$f(x) = x^2$ + bx + c$$ has its vertex at $$(2, -3). $$What is the value of $$b$$?

Accepted Answer

$$-4$$

Quadratic Functions and Parabolas: Vertex and Applications

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