Question 1

Which of the following is the correct quadratic formula for solving $$ax^2 + bx + c = 0$?

Accepted Answer

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

Question 2

Given the quadratic function $$f(x) = -2(x-3)^2$ + 5$$, what are the coordinates of the vertex?

Accepted Answer

$$(3, 5)$$

Question 3

If the leading coefficient $$a of a $$quadratic function $$f(x) = a(x-h)^2$ + k is $$negative, what does the graph do?

Accepted Answer

It opens downward.

Question 4

What is the axis of symmetry for the quadratic function $$f(x) = 2(x+1)^2$ - 4$$?

Accepted Answer

$$x = -1$$

Question 5

Solve the equation $$x^2 - 5x + 6 = 0$ by factoring.

Accepted Answer

$$x = 2,\ x = 3$$

Question 6

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 7

A ball is thrown upward and its height in meters after $$t$$ seconds is given by $$h(t) = -5t^2$ + 20t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 8

Which of the following describes the domain and range of $$f(x) = -3(x-1)^2$ + 4$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, 4]$$

Question 9

Given the graph of a parabola with vertex at $$(2, -3)$$ and passing through $$(3, 1)$$, what is the equation in vertex form?

Accepted Answer

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

Question 10

Which of the following is NOT a characteristic of the graph of a quadratic function?

Accepted Answer

It always opens upward.

Question 11

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 12

If $$f(x) = 2(x-1)^2$ + 3$$, what is the $$y-$$intercept?

Accepted Answer

$$f(0) = 2(0-1)^2$ + 3 = 2(1) + 3 = 5$$

Question 13

Which transformation occurs when the function $$f(x) = (x-2)^2$ is changed to g(x$$) = $$(x-2)^2 + 5$?

Accepted Answer

A vertical shift upward by 5 units.

Question 14

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

Accepted Answer

$$3$$

Question 15

Which of the following best describes the effect of the coefficient $$a in$$ $$f(x) = a(x-h)^2$ + k$$?

Accepted Answer

It determines the direction and width of the parabola.

Question 16

If the quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003e 0$$, what can you say about its range?

Accepted Answer

Range: $$[k, \infty)$$, where $$k is $$the minimum value.

Quadratic Functions: Concepts, Graphing, and Applications

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