Chapter Review
Chapter
Chapter 3
Section
Chapter Review
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Solutions 22 Videos

Match each factored form with the correct standard form.

a) \displaystyle f(x)=(x+3)(2 x-7)

b) \displaystyle f(x)=2(x+7)(x-3)

c) \displaystyle f(x)=(2 x+1)(x+7)

d) \displaystyle f(x)=(x+7)(x-3)

i) \displaystyle f(x)=x^{2}+4 x-21

ii) \displaystyle f(x)=2 x^{2}-x-21 iii) \displaystyle f(x)=2 x^{2}+8 x-42 iv) \displaystyle f(x)=2 x^{2}+15 x+7

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Q1

Determine the maximum or minimum of each function.

\displaystyle f(x)=x^{2}-2 x-35

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Q2a

Determine the maximum or minimum of each function.

\displaystyle f(x)=2 x^{2}+7 x+3

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Q2b

Determine the maximum or minimum of each function.

\displaystyle g(x)=-2 x^{2}+x+15

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Q2c

Determine the zeros and the maximum or minimum value for each function.

\displaystyle f(x)=x^{2}+2 x-15

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Q3a

Determine the zeros and the maximum or minimum value for each function.

\displaystyle f(x)=-x^{2}+8 x-7

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Q3b

Determine the zeros and the maximum or minimum value for each function.

\displaystyle f(x)=2 x^{2}+18 x+16

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Q3c

Determine the zeros and the maximum or minimum value for each function.

\displaystyle f(x)=2 x^{2}+7 x+3

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Q3d

Determine the zeros and the maximum or minimum value for each function.

\displaystyle f(x)=6 x^{2}+7 x-3

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Q3e

Determine the zeros and the maximum or minimum value for each function.

\displaystyle f(x)=-x^{2}+49

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Q3f

The function \displaystyle h(t)=1+4 t-1.86 t^{2} models the height of a rock thrown upward on the planet Mars, where \displaystyle h(t) is height in metres and \displaystyle t is time in seconds. Use a graph to determine a) the maximum height the rock reaches

b) how long the rock will be above the surface of Mars

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Q4

Determine the zeros, the coordinates of the vertex, and the \displaystyle y -intercept for each function.

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Q5a

Determine the zeros, the coordinates of the vertex, and the \displaystyle y -intercept for each function.

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Q5b

Solve by factoring.

\displaystyle x^{2}+2 x-35=0

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Q6a

Solve by factoring.

\displaystyle -x^{2}-5 x=-24

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Q6b

Solve by factoring.

\displaystyle 9 x^{2}=6 x-1

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Q6c

Solve by factoring.

\displaystyle 6 x^{2}=7 x+5

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Q6d

A firecracker is fired from the ground. The height of the firecracker at a given time is modelled by the function \displaystyle h(t)=-5 t^{2}+50 t , where \displaystyle h(t) is the height in metres and \displaystyle t is time in seconds. When will the firecracker reach a height of \displaystyle 45 \mathrm{~m} ?

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Q7

The population of a city, \displaystyle P(t) , is given by the function \displaystyle P(t)=14 t^{2}+820 t+42000 , where \displaystyle t is time in years. Note: \displaystyle t=0 corresponds to the year 2000 .

a) When will the population reach 56224 ? Provide your reasoning.

b) What will the population be in 2035 ? Provide your reasoning.

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Q8

Fred wants to install a wooden deck around his rectangular swimming pool. The function

\displaystyle C(x)=120 x^{2}+1800 x+5400 represents the cost of installation, where \displaystyle x is the width of the deck in metres and \displaystyle C(x) is the cost in dollars. What will the width be if Fred spends \displaystyle \$ 9480 for the deck? Here is Steve's solution.

\displaystyle [0

I used a graphing calculator to solve this problem. I entered \displaystyle 120 x^{2}+1800 x+5400 into \displaystyle Y 1 and 9480 into \displaystyle Y 2 to see where they intersect. They intersect at two places: \displaystyle x=2 and \displaystyle x=-17 . Since both answers must be positive, use \displaystyle x=2 and \displaystyle x=17 . Because you will get more deck with a higher number, use only \displaystyle x=17 .

Do you agree with his reasoning? Why or

why not?

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Q9

A toy rocket sitting on a tower is launched vertically upward. Its height \displaystyle y at time \displaystyle t is given in the table.

\displaystyle \begin{array}{|c|c|}\hline \boldsymbol{t} Time (s) & \boldsymbol{y} Height (\mathbf{m}) \\ \hline 0 & 16 \\ \hline 1 & 49 \\ \hline 2 & 60 \\ \hline 3 & 85 \\ \hline 4 & 88 \\ \hline 5 & 81 \\ \hline 6 & 64 \\ \hline 7 & 37 \\ \hline 8 & 0 \\ \hline\end{array}

a) What is an equation of a curve of good fit? b) How do you know that the equation in

part (a) is a good fit?

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Q10

Determine the equation of a curve of good fit for the scatter plot shown.

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Q11