Question 1

Which of the following is the vertex of the graph of $$f(x) = 3(x-2)^2$ + 5$$?

Accepted Answer

$$(2, 5)$$

Question 2

What is the equation of the axis of symmetry for the function $$f(x) = -4(x+1)^2$ - 7$$?

Accepted Answer

$$x = -1$$

Question 3

Which transformation describes how to obtain the graph of $$g(x) = (x-3)^2$ from f(x$$) = $$x^2$$?

Accepted Answer

Shift right 3 units

Question 4

Given $$f(x) = x^2$, which function represents a parabola that is wider than f(x$$)$$?

Accepted Answer

$$g(x) = \frac{1}{2}x^2$

Question 5

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

Accepted Answer

$$1$$

Question 6

Which of the following describes the graph of $$f(x) = 5x^2$ - 2$$ compared to $$g(x) = 5x^2$?

Accepted Answer

Shifted down 2 units

Question 7

A ball is thrown and its height in meters after $$t$$ seconds is given by $$h(t) = -4.9(t-2)^2$ + 10. $$What is the maximum height the ball reaches?

Accepted Answer

$$10$$ meters

Question 8

Which function has its vertex at $$(-3, -1)$$?

Accepted Answer

$$f(x) = (x+3)^2$ - 1$$

Question 9

If $$f(x) = x^2$ and g(x$$) = $$-2x^2$$, which statement is true about the graph of $$g(x)$$?

Accepted Answer

It opens downward and is narrower than $$f(x)$$

Question 10

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

Accepted Answer

It shifts the graph up if $$k \u003e 0$$ and down if $$k \u003c 0$$

Question 11

A company models its profit with $$P(x) = -3(x-5)^2$ + 20$$, where $$x is $$the number of items sold (in hundreds). What is the maximum profit?

Accepted Answer

$$20$$

Question 12

Which of the following functions represents a parabola that is shifted 4 units to the left and 3 units up from $$f(x) = x^2$?

Accepted Answer

$$f(x) = (x+4)^2$ + 3$$

Question 13

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

Accepted Answer

$$x = 1$$

Question 14

Which of the following best describes the graph of $$f(x) = -x^2$ + 4$$?

Accepted Answer

A parabola opening downward with vertex at $$(0, 4)$$

Question 15

If $$f(x) = 5(x-3)^2$ + 8$$, what is the minimum value of the function?

Accepted Answer

$$8$$

Question 16

Which of the following transformations will make the graph of $$f(x) = x^2$ both narrower and shifted down by 2 units?

Accepted Answer

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

Question 17

A medical researcher models the spread of a virus with $$N(t) = -2(t-6)^2$ + 50$$, where $$N is $$the number of cases and $$t is $$days since the outbreak. When does the maximum number of cases occur?

Accepted Answer

$$t = 6$$

Question 18

Which of the following functions is shifted 1 unit to the right and 7 units up from $$f(x) = 5x^2$?

Accepted Answer

$$g(x) = 5(x-1)^2$ + 7$$

Question 19

If $$f(x) = 2(x-3)^2$ + 1$$, what is the minimum value and where does it occur?

Accepted Answer

Minimum value is $$1 at$$ $$x = 3$$

Question 20

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

Accepted Answer

If $$|a| \u003e 1$$, the parabola is narrower; if $$0 \u003c |a| \u003c 1$$, it is wider

Quadratic Functions and Their Graphs: Section 8.6 Study Notes

Study Guide - Practice Questions

Study Guide - Flashcards