Question 1

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

Accepted Answer

$$(3, 5)$$

Question 2

Which of the following statements is TRUE about the graph of $$f(x) = 2(x + 1)^2$ - 4$$?

Accepted Answer

The parabola opens upward and has its vertex at $$(-1, -4).$$

Question 3

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

Accepted Answer

$$(2, 0)$$ and $$(4, 0)$$

Question 4

What is the axis of symmetry for the quadratic function $$f(x) = -x^2$ + 4x - 1$$?

Accepted Answer

$$x = 2$$

Question 5

A company models its profit with the function $$P(x) = -5x^2$ + 100x + 200$$, where $$x is $$the number of units sold. What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$1200 at$$ $$x = 10$$ units.

Question 6

Given $$f(x) = 3x^2$ - 12x + 7$$, what is the minimum value of the function?

Accepted Answer

$$-5$$

Question 7

Which of the following best describes the range of $$f(x) = -x^2$ + 2x + 3$$?

Accepted Answer

$$(-\infty, 4]$$

Question 8

If a quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003c 0$$, which of the following is always true?

Accepted Answer

The function has a maximum value at its vertex.

Question 9

A rectangular garden is to be fenced on all four sides with 80 meters of fencing. What dimensions maximize the area, and what is the maximum area?

Accepted Answer

Dimensions: $$20 m by$$ $$20 m$$; Maximum area: $$400 m$^2$$

Question 10

For the quadratic function $$f(x) = -2x^2$ + 8x - 3$$, what is the y-intercept?

Accepted Answer

$$(0, -3)$$

Question 11

Which of the following is the correct vertex form for the quadratic $$f(x) = x^2$ - 4x + 7$$?

Accepted Answer

$$f(x) = (x - 2)^2$ + 3$$

Question 12

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 13

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

Accepted Answer

$$x = 3$$

Question 14

Which of the following is NOT a characteristic of the graph of a quadratic function?

Accepted Answer

It always opens upward.

Question 15

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

Accepted Answer

Minimum value is $$-2 at$$ $$x = 2$$

Question 16

A quadratic function has its vertex at $$(4, -5)$$ and opens upward. Which of the following could be its equation?

Accepted Answer

$$f(x) = a(x - 4)^2$ - 5$$, where $$a \u003e 0$$

Question 17

Which of the following real-world scenarios can be modeled by a quadratic function?

Accepted Answer

The area of a rectangular garden with a fixed perimeter.

Question 18

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

Accepted Answer

$$9$$

Question 19

Which of the following steps is NOT part of the strategy for solving problems involving maximizing or minimizing quadratic functions?

Accepted Answer

Express the quantity as a function in two variables.

Quadratic Functions: Graphs, Properties, and Applications

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