Q: For the quadratic equation $$2x^2 + 3x - 2 = 0$, what are the x$-intercepts?

$$x = -2$$ \text{ and } $$x = \frac{1}{2}$$

Question 1

Which of the following is the standard form of a quadratic function?

Accepted Answer

$$f(x) = a(x-h)^2$ + k$$

Question 2

Given the quadratic function $$f(x) = -2(x-3)^2$ + 5$$, what is the vertex of the parabola?

Accepted Answer

$$(3, 5)$$

Question 3

For the quadratic function $$f(x) = 2x^2$ - 8x + 6$$, what is the axis of symmetry?

Accepted Answer

$$x = 2$$

Question 4

A ball is thrown and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 14t + 2. $$What is the maximum height the ball reaches?

Accepted Answer

$$22$$ meters

Question 5

Given $$f(x) = x^2$ - 6x + 8$$, find the $$x-$$intercepts.

Accepted Answer

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

Question 6

Which of the following best describes the domain and range of any quadratic function $$f(x) = ax^2$ + bx + c$$ where $$a 
eq 0$$?

Accepted Answer

Domain: all real numbers; Range: $$y \geq k or$$ $$y \leq k$$ depending on $$a$$

Question 7

The height of an arrow is modeled by $$f(x) = -0.005x^2$ + 2x + 5$$, where $$x is $$the horizontal distance in feet. At what horizontal distance does the arrow reach its maximum height?

Accepted Answer

$$x = 200$$ feet

Question 8

For the function $$f(x) = -x^2$ + 4x - 3$$, what is the $$y-$$intercept?

Accepted Answer

$$-3$$

Question 9

Chris has 120 feet of fencing to enclose a rectangular garden. What are the dimensions that maximize the area?

Accepted Answer

$$30 ft by$$ $$30 ft$$

Question 10

Among all pairs of numbers whose difference is $$8$$, which pair has the smallest possible product?

Accepted Answer

$$-4$$ and $$4$$

Question 11

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

Accepted Answer

$$-\frac{49}{8}$$

Question 12

If the graph of $$f(x) = a(x-h)^2$ + k$$ opens downward, which of the following must be true?

Accepted Answer

$$a \u003c 0$$

Question 13

A company models its profit with $$P(x) = -3x^2$ + 12x + 5$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$25$$

Question 14

Which transformation occurs when the function $$f(x) = x^2$ is changed to f(x$$) = $$(x-4)^2 + 3$?

Accepted Answer

Shift right $$4$$ units and up $$3$$ units

Question 15

For the quadratic equation $$2x^2 + 3x - 2 = 0$, what are the x$-intercepts?

Accepted Answer

$$x = -2$$ 	ext{ and } $$x = \frac{1}{2}$$

Question 16

If $$f(x) = -x^2$ + 6x - 7$$, what is the maximum value of $$f(x)$$ and at what $$x$$ does it occur?

Accepted Answer

Maximum value $$11 at$$ $$x = 3$$

Question 17

Which of the following is NOT a property of the graph of any quadratic function?

Accepted Answer

It always opens upward

Question 18

A rectangular field is to be fenced on three sides with 200 meters of fencing (the fourth side borders a river and needs no fence). What is the maximum area that can be enclosed?

Accepted Answer

$$5,000 m$^2$$

Question 19

If $$f(x) = -2(x+1)^2$ + 8$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 8]$$

Question 20

Which of the following steps is NOT necessary when graphing a quadratic function in standard form?

Accepted Answer

Find the slope at every point

Quadratic Functions: Graphs, Properties, and Applications

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