Question 1

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

Accepted Answer

$$f(x) = ax^2$ + bx + c$$

Question 2

Given the quadratic function $$f(x) = -2(x - 1)^2$ + 4$$, what are the coordinates of the vertex?

Accepted Answer

$$(1, 4)$$

Question 3

For the quadratic function $$f(x) = 4x^2$ - 16x + 1000$$, does the function have a minimum or maximum value, and at what $$x-$$value does it occur?

Accepted Answer

Minimum at $$x = 2$$

Question 4

What is the formula to find the $$x-$$coordinate of the vertex of a quadratic function in standard form $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

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

Question 5

A rectangular garden is to be enclosed with 120 feet of fencing. What dimensions will maximize the area of the garden?

Accepted Answer

30 ft by 30 ft

Question 6

Given $$f(x) = -3x^2$ + 6x - 1$$, what is the maximum value of the function?

Accepted Answer

$$f(1) = 2$$

Question 7

Which of the following statements is true about the graph of $$f(x) = ax^2$ + bx + c if$$ $$a \u003c 0$$?

Accepted Answer

The parabola opens downward and has a maximum value.

Question 8

If the vertex of a parabola is at $$(h, k)$$ and the equation is $$f(x) = a(x - h)^2$ + k$$, what does the value of $$a$$ determine?

Accepted Answer

The direction and width of the parabola

Question 9

A company models its profit with the function $$P(x) = -5x^2$ + 100x - 300$$, where $$x is $$the number of units sold. How many units should be sold to maximize profit?

Accepted Answer

$$x = 10$$

Question 10

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

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: depends on the vertex and direction of opening

Question 11

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

Accepted Answer

$$-2$$

Question 12

If a quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 19.6t + 2$$, what is the maximum height reached by the ball?

Accepted Answer

$$21.6$$ meters

Question 13

Which of the following is NOT a step in the strategy for maximizing or minimizing a quadratic function in a real-world problem?

Accepted Answer

Graph the function before expressing it in one variable

Question 14

A quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(3, -5). $$Which of the following could be the equation of the function?

Accepted Answer

$$f(x) = 2(x - 3)^2$ - 5$$

Question 15

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

Accepted Answer

Question 16

A quadratic function models the area $$A of a $$rectangle with a fixed perimeter of 40 meters. If the length is $$x$$ meters, which equation represents the area in terms of $$x$$?

Accepted Answer

$$A(x) = x(20 - x)$$

Quadratic Functions: Standard Form, Vertex, and Optimization

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