Question 1

Which of the following is the correct vertex of the quadratic function $$f(x) = 2x^2$ - 8x + 5$$?

Accepted Answer

$$(2, -3)$$

Question 2

A company models its profit (in thousands of dollars) by the function $$P(x) = -4x^2$ + 40x + 100$$, where $$x is $$the number of units produced (in hundreds). What is the maximum profit, and how many units should be produced to achieve it?

Accepted Answer

Maximum profit is $$300$$ thousand dollars at $$x = 5$$ hundred units.

Question 3

Given the quadratic function $$f(x) = -3(x-2)^2$ + 7$$, what is the range of $$f(x)$$?

Accepted Answer

$$(-\infty, 7]$$

Question 4

Which of the following statements is TRUE about the graph of $$f(x) = x^2$ + 6x + 13$$?

Accepted Answer

The parabola opens upward and does not cross the $$x-$$axis.

Question 5

A ball is thrown 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 at $$t = 2$$ seconds

Question 6

For the quadratic function $$f(x) = -x^2$ + 4x - 1$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2 \pm \sqrt{5}$$

Question 7

A farmer wants to build a rectangular pen along a straight river using $$120$$ meters of fencing for the other three sides (no fence along the river). What dimensions maximize the area of the pen?

Accepted Answer

Width $$= 30 m$$, Length $$= 60 m$$

Question 8

Given $$f(x) = (x+2)^2$ - 5$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$(0, -1)$$

Question 9

Which of the following best describes the domain and range of $$f(x) = -2x^2$ + 8x - 3$$?

Accepted Answer

Domain: $$(-\infty, +\infty)$$, Range: $$(-\infty, 5]$$

Question 10

A projectile is launched from a platform and its height is modeled by $$h(x) = -0.2x^2$ + 1.2x + 10$$, where $$x is $$the horizontal distance in meters. At what horizontal distance does the projectile reach its maximum height?

Accepted Answer

$$x = 3$$ meters

Question 11

If a quadratic function has its vertex at $$(5, -2)$$ and opens upward, which of the following could be its equation?

Accepted Answer

$$f(x) = (x-5)^2$ - 2$$

Question 12

Which of the following is the axis of symmetry for the function $$f(x) = 3x^2$ - 12x + 7$$?

Accepted Answer

$$x = 2$$

Question 13

A quadratic function $$f(x) = ax^2$ + bx + c$$ has no real $$x-$$intercepts. Which of the following must be true?

Accepted Answer

The discriminant $$b^2 - 4ac$$ \u003c 0$$

Question 14

Given $$f(x) = -2(x+1)^2$ + 5$$, what is the maximum value of $$f(x)$$ and where does it occur?

Accepted Answer

Maximum value is $$5 at$$ $$x = -1$$

Question 15

Which of the following is the correct standard form of the quadratic function with vertex at $$(3, 4)$$ and passing through the point $$(5, 0)$$?

Accepted Answer

Question 16

If $$f(x) = x^2$ - 4x + 7$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$3 at$$ $$x = 2$$

Question 17

A quadratic function models the height of a diver above water: $$h(t) = -4.9t^2$ + 9.8t + 3. $$How long after takeoff does the diver hit the water?

Accepted Answer

$$t = 2.236$$ seconds

Question 18

Which of the following is the correct interpretation of the vertex for the area function $$A(x) = -2x^2$ + 600x in $$the context of maximizing the area of a rectangular enclosure with $$600 ft of $$fencing along a river?

Accepted Answer

The vertex gives the width that maximizes area, which is $$150 ft.$$

Question 19

Given $$f(x) = x^2$ - 6x + 13$$, what is the minimum value of $$f(x)$$ and at what $$x$$ does it occur?

Accepted Answer

Minimum value is $$4 at$$ $$x = 3$$

Quadratic Functions and Parabola Analysis: Study Guide

Study Guide - Practice Questions

Study Guide - Flashcards