Chapter Review
Chapter
Chapter 3
Section
Chapter Review
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

Q1

Determine the maximum or minimum of each function.

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

Q2a

Determine the maximum or minimum of each function.

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

Q2b

Determine the maximum or minimum of each function.

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

Q2c

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

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

Q3a

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

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

Q3b

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

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

Q3c

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

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

Q3d

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

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

Q3e

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

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

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

Q4

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

Q5a

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

Q5b

Solve by factoring.

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

Q6a

Solve by factoring.

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

Q6b

Solve by factoring.

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

Q6c

Solve by factoring.

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

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}  ?

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.

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?

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?