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 $$f(x) = -2(x - 3)^2$ + 5$$, what is the vertex of the parabola?

Accepted Answer

$$(3, 5)$$

Question 3

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

Accepted Answer

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

Question 4

If the graph of a quadratic function opens downward, which of the following must be true about the coefficient $$a in$$ $$f(x) = a(x - h)^2$ + k$$?

Accepted Answer

$$a \u003c 0$$

Question 5

A ball is thrown upward and its height $$h (in $$meters) after $$t$$ seconds is modeled by $$h(t) = -4.9t^2$ + 19.6t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$21.2$$ meters

Question 6

Which of the following describes the axis of symmetry for the quadratic function $$f(x) = 2x^2$ - 8x + 5$$?

Accepted Answer

$$x = 2$$

Question 7

Given $$f(x) = x^2$ + 4x + 4$$, which method would be most efficient to solve $$f(x) = 0$$?

Accepted Answer

Factoring

Question 8

A company models its profit $$P (in $$thousands of dollars) by $$P(x) = -3x^2$ + 12x + 5$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit?

Accepted Answer

$$29$$ thousand dollars

Question 9

Which of the following is the quadratic formula used to solve $$ax^2 + bx + c = 0$?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 10

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

Accepted Answer

$$-2$$

Question 11

Which step is NOT part of the process for graphing a quadratic function in standard form?

Accepted Answer

Multiply the function by a constant to change its direction

Question 12

Given $$f(x) = (x + 1)^2$ - 9$$, what are the x-intercepts?

Accepted Answer

$$x = 2$$ and $$x = -4$$

Question 13

A bridge is designed so that its arch follows the equation $$y = -0.5(x - 10)^2$ + 25. $$What is the maximum height of the arch?

Accepted Answer

$$25$$ units

Question 14

If $$f(x) = x^2$ - 6x + 8$$, what are the solutions to $$f(x) = 0$$?

Accepted Answer

$$x = 2$$ and $$x = 4$$

Question 15

Which of the following statements is true about the graph of $$f(x) = a(x - h)^2$ + k$$ when $$a \u003e 0$$?

Accepted Answer

The parabola opens upward and $$k is $$its minimum value.

Question 16

A quadratic function models the height of a rocket: $$h(t) = -5t^2$ + 40t + 10. $$How many seconds after launch does the rocket reach its maximum height?

Accepted Answer

$$4$$ seconds

Question 17

Which of the following is the axis of symmetry for the graph of $$f(x) = x^2$ - 4x + 7$$?

Accepted Answer

$$x = 2$$

Question 18

If the quadratic equation $$x^2 + 2x + 4 = 0$ is solved using the quadratic formula, what type of solutions will you get?

Accepted Answer

Two complex solutions

Question 19

Which of the following is the correct process to find the vertex of $$f(x) = ax^2$ + bx + c$$?

Accepted Answer

Calculate $$x = -\frac{b}{2a}$$, then substitute into $$f(x) to $$find $$y$$

Question 20

A quadratic function $$f(x)$$ has its vertex at $$(2, -3)$$ and opens upward. Which of the following could be its equation?

Accepted Answer

$$f(x) = a(x - 2)^2$ - 3$$ where $$a \u003e 0$$

Quadratic Functions: Concepts, Graphing, and Solution Methods

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