Question 1

Given the quadratic function $$f(x) = (x + 2)^2$ - 1$$, what is the equation of the axis of symmetry?

Accepted Answer

$$x = -2$$

Question 2

For the function $$f(x) = (x + 2)^2$ - 1$$, what is the vertex of the parabola?

Accepted Answer

$$(-2, -1)$$

Question 3

What is the $$y-$$intercept of the function $$f(x) = (x + 2)^2$ - 1$$?

Accepted Answer

$$f(0) = 3$$

Question 4

Which of the following best describes the domain of $$f(x) = (x + 2)^2$ - 1$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 5

What is the range of the function $$f(x) = (x + 2)^2$ - 1$$?

Accepted Answer

$$[-1, \infty)$$

Question 6

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

Accepted Answer

Question 7

Given the quadratic function $$f(x) = (x + 2)^2$ - 1$$, which of the following points is an $$x-$$intercept?

Accepted Answer

Question 8

If the graph of $$f(x) = (x + 2)^2$ - 1 is $$shifted 3 units up, what is the new equation?

Accepted Answer

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

Question 9

Which transformation occurs when the function $$f(x) = (x + 2)^2$ - 1 is $$changed to $$f(x) = (x - 2)^2$ - 1$$?

Accepted Answer

Question 10

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

Accepted Answer

$$18$$ thousand dollars

Question 11

Which of the following statements is true about the graph of $$f(x) = (x + 2)^2$ - 1$$?

Accepted Answer

The parabola opens upward

Question 12

If $$f(x) = (x + 2)^2$ - 1$$, what is the value of $$x$$ where $$f(x) = 0$$?

Accepted Answer

$$x = -1$$ and $$x = -3$$

Question 13

A parabola has its vertex at $$(h, k)$$ and opens upward. Which of the following is always true about its range?

Accepted Answer

$$[k, \infty)$$

Question 14

The axis of symmetry for the quadratic function $$f(x) = ax^2$ + bx + c is $$given by which formula?

Accepted Answer

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

Question 15

If the graph of $$f(x) = (x + 2)^2$ - 1 is $$reflected over the $$x-$$axis, what is the new equation?

Accepted Answer

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

Question 16

A quadratic function models the height of a rocket: $$h(t) = -4.9t^2$ + 49t + 2. $$How many seconds after launch does the rocket reach its maximum height?

Accepted Answer

$$t = 5$$ seconds

Question 17

Which of the following best describes the effect of increasing the coefficient $$a in$$ $$f(x) = a(x + 2)^2$ - 1 ($$with $$a \u003e 0$$)?

Accepted Answer

The parabola becomes narrower

Question 18

If $$f(x) = (x + 2)^2$ - 1$$ represents the profit (in thousands of dollars) for $$x$$ years since a product launch, what is the minimum possible profit?

Accepted Answer

$$-1$$ thousand dollars

Question 19

A parabola passes through the points $$(-2, -1)$$ and $$(0, 3). If $$its axis of symmetry is $$x = -2$$, what is its equation?

Accepted Answer

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

Question 20

Which of the following is NOT a possible $$x-$$intercept of $$f(x) = (x + 2)^2$ - 1$$?

Accepted Answer

$$(0, 0)$$

Quadratic Functions: Graphs, Vertex, Intercepts, and Axis of Symmetry

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