Q: Which of the following describes the end behavior of $f(x) = -x^2 + 3$?

$f(x) \to -\infty$ as $x \to \pm\infty$

Question 1

Which of the following is the correct vertex 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 function $f(x) = 2x^2 - 8x + 7$, what is the axis of symmetry?

Accepted Answer

$x = 2$

Question 4

A parabola opens downward and has its vertex at $(1, 4)$. Which of the following could be its equation?

Accepted Answer

$f(x) = -3(x - 1)^2 + 4$

Question 5

What is the range of the function $f(x) = 5(x - 2)^2 - 7$?

Accepted Answer

$[-7, \infty)$

Question 6

If a quadratic function has its vertex at $(0, -3)$ and opens upward, which statement is true?

Accepted Answer

The function has a minimum at $y = -3$

Question 7

Given $f(x) = x^2 + 6x + 7$, what is the vertex form of the function?

Accepted Answer

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

Question 8

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

Accepted Answer

Shift right 4 units and up 2 units

Question 9

A real-world scenario: The height $h$ (in meters) of a ball thrown upward is modeled by $h(t) = -5t^2 + 20t + 2$. What is the maximum height the ball reaches?

Accepted Answer

$18$ meters

Question 10

Which of the following statements about the domain of any quadratic function $f(x) = ax^2 + bx + c$ is true?

Accepted Answer

The domain is all real numbers

Question 11

Given $f(x) = -x^2 + 4x - 1$, what is the interval where the function is increasing?

Accepted Answer

$(-\infty, 2)$

Question 12

If $f(x) = 3x^2 + 12x$, what is the $y$-intercept of the function?

Accepted Answer

$0$

Question 13

Which method is most appropriate to solve $x^2 - 9 = 0$?

Accepted Answer

Square root property

Question 14

For the quadratic function $f(x) = a(x - h)^2 + k$, what does the parameter $a$ control?

Accepted Answer

The direction and width of the parabola

Question 15

A company models its profit with $P(x) = -2x^2 + 8x + 10$, where $x$ is the number of units sold (in thousands). What number of units maximizes profit?

Accepted Answer

$x = 2$

Question 16

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

Accepted Answer

$f(x) 	o -\infty$ as $x 	o \pm\infty$

Question 17

Given $f(x) = (x + 2)^2 - 4$, what are the $x$-intercepts?

Accepted Answer

$x = -2 \pm 2$

Question 18

If the graph of $f(x) = x^2$ is reflected over the $x$-axis and shifted down 3 units, what is the new equation?

Accepted Answer

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

Question 19

Which of the following is NOT a possible number of turning points for a quadratic function?

Accepted Answer

2

Question 20

A quadratic function models the height of a projectile. If the function is $h(t) = -16t^2 + 32t + 5$, at what time does the projectile hit the ground?

Accepted Answer

$t = 2.13$

Quadratic Functions: Properties, Vertex Form, and Graphing Techniques

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