Question 1

Given the equation $$y = x^2$ - 4$$, which of the following describes the transformation applied to the parent function $$y = x^2$?

Accepted Answer

A vertical shift 4 units down

Question 2

Which of the following is the vertex of the parabola given by $$y = (x + 3)^2$ + 2$$?

Accepted Answer

$$(-3, 2)$$

Question 3

If the graph of $$y = x^2$ is reflected over the x-axis and shifted 5 units up, what is the new equation?

Accepted Answer

$$y = -x^2$ + 5$$

Question 4

Which equation represents a parabola that opens downward and has its vertex at $$(2, -3)$$?

Accepted Answer

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

Question 5

A company models its profit with the function $$P(x) = -2x^2$ + 8x + 10$$, where $$x is $$the number of units sold (in thousands). What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$18 at$$ $$x = 2$$

Question 6

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

Accepted Answer

It determines the direction and width of the parabola

Question 7

Given the function $$f(x) = (x - 1)^2$ - 9$$, what is the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 8

If $$y = (x + 2)^2$ - 5 is $$graphed, which point is guaranteed to be on the graph?

Accepted Answer

$$(-2, -5)$$

Question 9

A ball is thrown upward and its height (in meters) after $$t$$ seconds is given by $$h(t) = -4.9t^2$ + 14t + 2. $$What is the maximum height reached by the ball?

Accepted Answer

$$22$$ meters

Question 10

Which transformation will change the graph of $$y = x^2$ to y = (x$$ - $$4)^2 + 7$?

Accepted Answer

Shift right 4 units and up 7 units

Precalculus Graphing Worksheet Guidance

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