Question 1

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

Accepted Answer

$$f(x) = a(x-h)^2$ + k$$

Question 2

Given the quadratic function $$f(x) = 2x^2$ + 8x - 10$$, what are the coordinates of its vertex?

Accepted Answer

$$(-2, -18)$$

Question 3

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

Accepted Answer

Whether the parabola opens up or down

Question 4

A farmer wants to build a rectangular pen using a straight wall for one side and 100 feet of fencing for the other three sides. What is the maximum area that can be enclosed?

Accepted Answer

$$1250$$ square feet

Question 5

What is the axis of symmetry for the function $$f(x) = 2x^2$ + 8x - 10$$?

Accepted Answer

$$x = -2$$

Question 6

If a quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003c 0$$, what can you conclude about its graph?

Accepted Answer

The parabola opens downward and has a maximum value.

Question 7

Given the quadratic function $$f(x) = -2x^2$ + 8x - 5$$, what is the range of $$f$$?

Accepted Answer

$$(-\infty, 3]$$ where $$3 is $$the maximum value

Question 8

Which of the following is the correct formula for the x-coordinate of the vertex of $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

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

Question 9

A quadratic function has its vertex at $$(3, -5)$$ and opens upward. Which of the following could be its equation?

Accepted Answer

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

Question 10

If the quadratic function $$f(x) = ax^2$ + bx + c$$ has no real x-intercepts, what does this imply about its graph?

Accepted Answer

The parabola does not cross the x-axis.

Question 11

Given $$f(x) = a(x-h)^2$ + k$$, what is the y-intercept of the function?

Accepted Answer

$$f(0) = a(-h)^2$ + k$$

Question 12

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 steps is NOT part of the procedure for graphing a quadratic function in standard form?

Accepted Answer

Calculate the slope at every point.

Question 14

If $$f(x) = 3(x+2)^2$ - 5$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$-5$$

Question 15

A quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003e 0. $$Which statement is true?

Accepted Answer

The function has a minimum value at its vertex.

Question 16

Given the quadratic function $$f(x) = -2x^2$ + 8x - 5$$, solve the inequality $$-2x^2 + 8x - 5$$ \u003e 0$$.

Accepted Answer

$$0.7 \u003c x \u003c 3.6$$

Question 17

If a quadratic function $$f(x) = ax^2$ + bx + c$$ has its vertex at $$(h, k)$$, which of the following is always true?

Accepted Answer

The axis of symmetry is $$x = h$$

Question 18

A company models its profit $$P(x) in $$thousands of dollars by $$P(x) = -5x^2$ + 40x - 60$$, where $$x is $$the number of units sold in thousands. What is the maximum profit?

Accepted Answer

$$100$$ thousand dollars

Question 19

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

Accepted Answer

The area of a rectangular pen with a fixed perimeter

Quadratic Functions: Graphing, Properties, and Applications

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