Question 1

Given the quadratic function $$f(x) = 3x^2$ - 12x + 7$$, what are the coordinates of the vertex?

Accepted Answer

$$(2, -5)$$

Question 2

A ball is launched from a platform with an initial velocity of $$80 ft/s $$from a height of $$100 ft. $$Its height after $$t$$ seconds is given by $$S(t) = -16t^2$ + 80t + 100. At $$what time does the ball reach its maximum height?

Accepted Answer

$$t = 2.5$$ seconds

Question 3

For the quadratic function $$f(x) = -x^2$ + 6x - 8$$, what is the maximum value of the function?

Accepted Answer

$$1$$

Question 4

Which of the following is the correct solution to the system of equations: $$\begin{cases} 2x + 3y = 7 \ 4x - 3y = 5 \end{cases}$$?

Accepted Answer

$$(2, 1)$$

Question 5

A company finds that its profit $$P(x) in $$thousands of dollars from selling $$x$$ hundred units is given by $$P(x) = -2x^2$ + 12x - 7. $$What is the maximum profit, and how many units should be sold to achieve it?

Accepted Answer

Maximum profit is $$25$$ thousand dollars at $$x = 3$$ hundred units

Question 6

Given the quadratic $$f(x) = 2x^2$ + 8x + 6$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = -2 + \sqrt{2}, x = -2 - \sqrt{2}$$

Question 7

A projectile is launched from the ground with an initial velocity of $$32 ft/s. $$Its height is given by $$S(t) = -16t^2$ + 32t. At $$what time does it return to the ground?

Accepted Answer

$$t = 2$$ seconds

Question 8

Solve the system: $$\begin{cases} x + 2y = 5 \ 3x - y = 4 \end{cases}$$

Accepted Answer

$$(2, 1.5)$$

Question 9

A theater sold $$1,200$$ tickets, with twice as many student tickets as adult tickets. How many student tickets were sold?

Accepted Answer

$$800$$

Question 10

Given $$f(x) = -3x^2$ + 12x - 5$$, does the parabola open upward or downward, and what is the $$y-$$intercept?

Accepted Answer

Opens downward; $$y-$$intercept is $$-5$$

Question 11

A ball is thrown upward from a $$50 ft $$platform with an initial velocity of $$32 ft/s. $$Its height is $$S(t) = -16t^2$ + 32t + 50. $$What is the maximum height reached by the ball?

Accepted Answer

$$82 ft$$

Question 12

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

Accepted Answer

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

Question 13

If $$f(x) = x^2$ - 6x + 8$$, what are the $$x-$$intercepts?

Accepted Answer

$$x = 2, x = 4$$

Question 14

A system of equations is given by $$\begin{cases} 5x + 2y = 18 \ 3x - 2y = 6 \end{cases}. $$What is the solution?

Accepted Answer

$$(3, 1.5)$$

Question 15

A quadratic function models the height of a rocket: $$h(t) = -16t^2$ + 128t + 400. $$What is the maximum height reached by the rocket?

Accepted Answer

$$704 ft$$

Question 16

Given the system $$\begin{cases} 4x + 4y = 3 \ 2x = 2y + 8 \end{cases}$$, what is the value of $$y$$?

Accepted Answer

$$y = -\dfrac{13}{8}$$

Question 17

If a quadratic function $$f(x) = ax^2$ + bx + c$$ has $$a \u003c 0$$, which of the following statements is true?

Accepted Answer

The parabola opens downward and has a maximum at its vertex.

Question 18

A store sells $$x$$ apples and $$y$$ oranges. If $$x + y = 50$$ and apples cost $$\2$ each while oranges cost $$\$$3$$ each, and the total revenue is $$\120$, how many apples were sold?

Accepted Answer

$$20$$

Question 19

For the quadratic $$f(x) = 4x^2$ - 12x + 9$$, what is the $$y-$$intercept?

Accepted Answer

$$9$$

Question 20

A ball is thrown upward from a $$20 ft $$platform with an initial velocity of $$24 ft/s. $$Its height is $$S(t) = -16t^2$ + 24t + 20. $$How long does it take for the ball to hit the ground?

Accepted Answer

$$2.8$$ seconds

Quadratic Functions and Systems of Linear Equations: Study Guide for College Algebra

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