Question 1

Given the quadratic function $$f(x) = -2(x-3)^2$ + 4$$, what are the coordinates of the vertex?

Accepted Answer

$$(3, 4)$$

Question 2

Which of the following best describes the axis of symmetry for the quadratic function $$f(x) = 2x^2$ - 8x + 5$$?

Accepted Answer

$$x = 2$$

Question 3

A ball is thrown upward from a platform 20 meters high with an initial velocity of 12 m/s. Its height after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 12t + 20. $$What is the maximum height the ball reaches?

Accepted Answer

$$27.35$$ meters

Question 4

What is the discriminant of the quadratic equation $$2x^2 - 4x + 3 = 0$ and how many real x$-intercepts does the graph have?

Accepted Answer

Discriminant $$= -8$$, no real $$x-$$intercepts

Question 5

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

Accepted Answer

$$(x-2)(x-3)$$

Question 6

A rectangular garden is to be fenced on three sides (the fourth side is against a wall) using 120 meters of fencing. If the width is $$x$$, what value of $$x$$ maximizes the area?

Accepted Answer

$$x = 30$$ meters

Question 7

Given $$f(x) = -x^2$ + 6x - 5$$, what is the range of the function?

Accepted Answer

$$(-\infty, 4]$$

Question 8

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

Accepted Answer

The parabola opens downward

Question 9

If a quadratic function has a vertex at $$(2, -3)$$ and passes through the point $$(4, 5)$$, which is the correct equation for the function?

Accepted Answer

$$f(x) = 2(x-2)^2$ - 3$$ where $$a = 2$$ found by solving $$5 = a(4-2)^2$ - 3$$

Question 10

Which of the following is the correct quadratic formula for finding the $$x-$$intercepts of $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 11

A company wants to build an open-top box with a square base by cutting equal squares from each corner of a 20 cm by 20 cm piece of cardboard and folding up the sides. If the volume must be $$200 cm$^3$$, what is the equation relating the side of the cut square $$x to $$the volume?

Accepted Answer

$$(20-2x)^2 x = 200$

Question 12

Given $$f(x) = 3x^2$ - 6x + 2$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$(0, 2)$$

Question 13

If the discriminant $$b^2 - 4ac$ of a quadratic equation is zero, what does this indicate about the graph of the function?

Accepted Answer

The graph touches the $$x-$$axis at one point

Question 14

A projectile is launched and its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 64t + 80. $$How long does it take to reach its maximum height?

Accepted Answer

$$t = 2$$ seconds

Question 15

Which of the following best describes the domain of any quadratic function $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 16

Given $$f(x) = (x-1)(x+3)$$, what are the $$x-$$intercepts of the function?

Accepted Answer

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

Question 17

A garden measuring 14 meters by 12 meters is to have a path of uniform width $$x$$ around it. If the total area (garden plus path) is $$357$$ square meters, which equation can be used to solve for $$x$$?

Accepted Answer

$$(14 + 2x)(12 + 2x) = 357$$

Question 18

If $$f(x) = -x^2$ + 4x - 1$$, what is the maximum value of $$f(x)$$?

Accepted Answer

$$3$$

Question 19

Which of the following is NOT a possible number of $$x-$$intercepts for a quadratic function?

Accepted Answer

Three

D2-D4

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