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

For the quadratic function $$f(x) = -x^2$ + 8x - 12$$, determine the axis of symmetry.

Accepted Answer

$$x = 4$$

Question 3

A company models its profit with $$P(x) = -2x^2$ + 16x + 5$$, where $$x is $$the number of units sold. What is the maximum profit?

Accepted Answer

$$69$$

Question 4

Which of the following describes the graph of $$f(x) = -3(x + 2)^2$ + 7$$?

Accepted Answer

A parabola opening downward with vertex $$(-2, 7)$$

Question 5

Find the minimum value of $$g(x) = x^2$ - 6x + 11.$$

Accepted Answer

$$2$$

Question 6

A farmer wants to fence a rectangular garden against a barn using 40 meters of fencing for the other three sides. What is the maximum area that can be enclosed?

Accepted Answer

$$133.33$$ square meters

Question 7

Given $$f(x) = x^2$ + 4x + 1$$, rewrite the function in vertex form by completing the square.

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

If $$f(x) = 3x^2$ - 12x + 7$$, on which interval is the function increasing?

Accepted Answer

$$(2, \infty)$$

Question 10

A landscaper has 24 ft of stone to enclose a rectangular pond next to a wall (the wall forms one side). What width gives the maximum area?

Accepted Answer

$$6 ft$$

Question 11

Given $$f(x) = -2x^2$ + 4x + 1$$, what is the range of the function?

Accepted Answer

$$(-\infty, 3]$$

Question 12

Which transformation occurs when the graph of $$y = x^2$ is changed to y = (x$$ - $$5)^2 + 2$?

Accepted Answer

Shift right 5 units and up 2 units

Question 13

For $$f(x) = x^2$ + 10x + 23$$, what is the axis of symmetry?

Accepted Answer

$$x = -5$$

Question 14

If $$g(x) = \frac{1}{2}(x - 4)^2$, what is the minimum value of g(x$$)$$?

Accepted Answer

$$0$$

Question 15

Given $$f(x) = -x^2$ + 14x - 47$$, what is the interval where the function is decreasing?

Accepted Answer

$$(7, \infty)$$

Question 16

A quadratic function $$f(x) = ax^2$ + bx + c$$ opens upward if:

Accepted Answer

$$a \u003e 0$$

Question 17

Which of the following is the vertex of $$f(x) = x^2$ - 8x + 20$$?

Accepted Answer

$$(4, 4)$$

Question 18

If the vertex of a parabola is $$(h, k)$$, what is the equation of its axis of symmetry?

Accepted Answer

$$x = h$$

Question 19

A quadratic function models the height $$h (in $$meters) of a ball thrown upward: $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached?

Accepted Answer

$$22$$ meters

Question 20

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

Accepted Answer

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

Analyzing Graphs of Quadratic Functions (Section 3.3)

Guida di studio - Domande di pratica

Study guide - Flashcard