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

$a > 0$

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)

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