Question 1

Given the function $$f(x) = x^2$ - 4$$, for which values of $$x is$$ $$f(x)$$ negative?

Accepted Answer

$$-2 \u003c x \u003c 2$$

Question 2

What are the zeroes of the quadratic function $$f(x) = 2x^2$ - 3x - 2$$?

Accepted Answer

$$x = -0.5$$ and $$x = 2$$

Question 3

For the function $$f(x) = x^2$ - 4$$, what is the vertex of the parabola?

Accepted Answer

$$(0, -4)$$

Question 4

A golf ball's height after $$t$$ seconds is given by $$s(t) = -16t^2$ + 64t + 4. $$For what interval of $$t is $$the ball higher than $$52 ft $$above ground?

Accepted Answer

$$1 \u003c t \u003c 3$$

Question 5

A circle has an area of at least $$225\pi. $$What is the minimum possible diameter of the circle?

Accepted Answer

$$15$$

Question 6

Which transformation shifts the graph of $$f(x) = |x|$$ two units to the right?

Accepted Answer

$$f(x) = |x-2|$$

Question 7

What is the effect of multiplying the function $$f(x) = |x| by$$ $$\frac{1}{3}$$?

Accepted Answer

The graph shrinks vertically by a factor of $$3$$

Question 8

Given the function $$f(x) = |x+4| - 1$$, what is the vertex of the graph?

Accepted Answer

$$(-4, -1)$$

Question 9

If the graph of $$f(x) = \sqrt{x} is $$reflected over the $$x-$$axis, shifted up $$2$$ units, and right $$2$$ units, what is the equation of the new graph?

Accepted Answer

$$f(x) = -\sqrt{x-2} + 2$$

Question 10

For the quadratic $$f(x) = 2x^2$ - 3x - 2$$, for which intervals is $$f(x) \leq 0$$?

Accepted Answer

$$-0.5 \leq x \leq 2$$

Question 11

Which of the following describes a vertical shift of the graph $$f(x) = |x| up by$$ $$2$$ units?

Accepted Answer

$$f(x) = |x| + 2$$

Question 12

If $$f(x) = x^2$ - 4$$, what is the $$y-$$intercept of the graph?

Accepted Answer

$$(0, -4)$$

Question 13

Which transformation will move the vertex of $$f(x) = |x| to$$ $$(-2, 2)$$?

Accepted Answer

$$f(x) = |x+2| + 2$$

Question 14

Which equation represents a horizontal shrink of $$f(x) = |x| by a $$factor of $$3$$?

Accepted Answer

$$f(x) = |3x|$$

Question 15

For the function $$f(x) = x^2$ - 4$$, when is $$f(x) \geq 0$$?

Accepted Answer

$$x \leq -2 or$$ $$x \geq 2$$

Question 16

If the graph of $$f(x) = |x| is $$shifted left $$4$$ units and down $$1$$ unit, what is the equation of the new graph?

Accepted Answer

$$f(x) = |x+4| - 1$$

Question 17

Which of the following is the correct factored form of $$x^2 - 4$?

Accepted Answer

$$(x-2)(x+2)$$

Question 18

If $$f(x) = |x|$$, what is the effect of replacing $$x$$ with $$x-2 in $$the function?

Accepted Answer

The graph shifts right $$2$$ units

Question 19

For the function $$f(x) = 2x^2$ - 3x - 2$$, what is the $$y-$$intercept?

Accepted Answer

$$(0, -2)$$

Quadratic Functions, Inequalities, and Transformations of Graphs

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