Purchase this Material for $10

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

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 `

Buy to View

Plus Content!
Q1

Determine the maximum or minimum of each function.

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

Buy to View

Plus Content!
Q2a

Determine the maximum or minimum of each function.

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

Buy to View

Plus Content!
Q2b

Determine the maximum or minimum of each function.

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

Buy to View

Plus Content!
Q2c

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

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

Buy to View

Plus Content!
Q3a

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

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

Buy to View

Plus Content!
Q3b

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

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

Buy to View

Plus Content!
Q3c

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

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

Buy to View

Plus Content!
Q3d

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

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

Buy to View

Plus Content!
Q3e

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

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

Buy to View

Plus Content!
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

Buy to View

Plus Content!
Q4

Determine the zeros, the coordinates of the vertex, and the `\displaystyle y `

-intercept for each function.

Buy to View

Plus Content!
Q5a

`\displaystyle y `

-intercept for each function.

Buy to View

Plus Content!
Q5b

Solve by factoring.

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

Buy to View

Plus Content!
Q6a

Solve by factoring.

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

Buy to View

Plus Content!
Q6b

Solve by factoring.

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

Buy to View

Plus Content!
Q6c

Solve by factoring.

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

Buy to View

Plus Content!
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} `

?

Buy to View

Plus Content!
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.

Buy to View

Plus Content!
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?

Buy to View

Plus Content!
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?

Buy to View

Plus Content!
Q10

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

Buy to View

Plus Content!
Q11