Question 1

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

Accepted Answer

$$(-3, -2)$$

Question 2

For the function $$f(x) = -2(x - 1)^2$ + 3$$, what is the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 3

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

Accepted Answer

The parabola opens downward and has a maximum at $$(h, k).$$

Question 4

Find the vertex of the quadratic function $$f(x) = x^2$ + 10x + 23.$$

Accepted Answer

$$(-5, -2)$$

Question 5

A stone is thrown upward from a height of 30 ft with an initial velocity of 60 ft/sec. Its height after $$t$$ seconds is given by $$h(t) = -16t^2$ + 60t + 30. At $$what time does the stone reach its maximum height?

Accepted Answer

$$t = 1.875$$ seconds

Question 6

Given $$f(x) = ax^2$ + bx + c$$, what is the formula for the $$x-$$coordinate of the vertex?

Accepted Answer

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

Question 7

A landscaper has 24 ft of stone to enclose three sides of a rectangular pond (the fourth side is a wall). What dimensions maximize the area?

Accepted Answer

Width $$= 6 ft$$, Length $$= 12 ft$$

Question 8

For the function $$f(x) = -x^2$ + 14x - 47$$, what is the range?

Accepted Answer

$$(-\infty, k]$$ where $$k is $$the maximum value at the vertex

Question 9

If $$f(x) = 3(x - 2)^2$ + 5$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$5$$

Question 10

Which of the following best describes the interval(s) where $$f(x) = x^2$ + 10x + 23 is $$increasing?

Accepted Answer

$$(-5, \infty)$$

Question 11

Given $$f(x) = -2(x + 4)^2$ + 7$$, what is the maximum value of $$f(x)$$?

Accepted Answer

$$7$$

Question 12

Which of the following is the correct vertex form for $$f(x) = x^2$ + 10x + 23$$?

Accepted Answer

$$f(x) = (x + 5)^2$ - 2$$

Question 13

A ball is thrown upward and its height is modeled by $$h(t) = -16t^2$ + 64t + 80. $$What is the maximum height reached by the ball?

Accepted Answer

$$144 ft$$

Question 14

For $$f(x) = a(x - h)^2$ + k$$, which parameter determines the direction the parabola opens?

Accepted Answer

$$a$$

Question 15

If the axis of symmetry of a parabola is $$x = 4$$ and the vertex is at $$(4, -7)$$, which could be the equation of the parabola?

Accepted Answer

$$f(x) = 2(x - 4)^2$ - 7$$

Question 16

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

Accepted Answer

The height of a projectile over time after being launched upward.

Question 17

Given $$f(x) = -x^2$ + 14x - 47$$, at what $$x-$$value does the maximum occur?

Accepted Answer

$$x = 7$$

Question 18

If $$f(x) = x^2$ - 6x + 8$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-1$$

Question 19

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

Accepted Answer

The parabola becomes narrower.

Analyzing Graphs of Quadratic Functions: Vertex, Axis of Symmetry, and Extrema

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