Question 1

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

Accepted Answer

$$(3, 8)$$

Question 2

Which of the following best describes the axis of symmetry for the quadratic function $$f(x) = 4x^2$ - 8x + 5$$?

Accepted Answer

$$x = 1$$

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 100 meters of fencing. If the length parallel to the wall is $$x$$, what value of $$x$$ maximizes the area?

Accepted Answer

$$50$$ meters

Question 7

Given $$f(x) = x^2$ + 6x + 8$$, what are the $$x-$$intercepts?

Accepted Answer

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

Question 8

Which of the following statements is true about the graph of $$f(x) = -3x^2$ + 12x - 7$$?

Accepted Answer

It opens downward and has a maximum value.

Question 9

If a quadratic function has a vertex at $$(2, -5)$$ and passes through the point $$(4, 3)$$, which of the following could be its equation?

Accepted Answer

Question 10

Which of the following is the range of the function $$f(x) = -x^2$ + 4x - 1$$?

Accepted Answer

$$(-\infty, 3]$$

Question 11

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(1, -4)$$ and passes through $$(3, 0). If$$ $$a = 1$$, what is the value of $$b$$?

Accepted Answer

$$b = -6$$

Question 12

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

Accepted Answer

If $$|a| \u003e 1$$, the parabola is narrower; if $$0 \u003c |a| \u003c 1$$, it is wider.

Question 13

A projectile is launched from a height of 50 meters with an initial velocity of 20 m/s. Its height after $$t$$ seconds is $$h(t) = -4.9t^2$ + 20t + 50. $$How long does it take to hit the ground?

Accepted Answer

$$t \approx 5.23$$ seconds

Question 14

Given $$f(x) = (x+1)^2$ - 9$$, what are the $$x-$$intercepts?

Accepted Answer

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

Question 15

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 16

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

Accepted Answer

The graph touches the $$x-$$axis at one point (one real root).

Question 17

A box with no top is to be made from a $$20 cm by$$ $$20 cm $$square by cutting equal squares from each corner and folding up the sides. If the volume must be $$200 cm$^3$$, what size square should be cut from each corner?

Accepted Answer

$$x = 2 cm$$

Question 18

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

Accepted Answer

$$4$$

Question 19

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

Accepted Answer

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

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