Chapter Test
Chapter
Chapter 3
Section
Chapter Test
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Solutions 12 Videos

Write in standard form.

a) \displaystyle f(x)=(3 x-5)(2 x-9) \quad b) \displaystyle f(x)=(6-5 x)(x+2)

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Q1

Write in factored form.

\displaystyle f(x)=x^{2}-81

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Q2a

Write in factored form.

\displaystyle f(x)=6 x^{2}+5 x-4

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Q2b

Determine the zeros, the axis of symmetry, and the maximum or minimum value for each function.

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

b) \displaystyle f(x)=-4 x^{2}-12 x+7

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Q3

Can all quadratic equations be solved by factoring? Explain.

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Q4

Solve by graphing.

\displaystyle x^{2}+6 x-3=-3

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Q5a

Solve by graphing.

\displaystyle 2 x^{2}-5 x=7

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Q5b

Solve by factoring.

\displaystyle 2 x^{2}+11 x-6=0

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Q6a

Solve by factoring.

\displaystyle x^{2}=4 x+21

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Q6b

The population of a town, \displaystyle P(t) , is modelled by the function \displaystyle P(t)=6 t^{2}+110 t+3000 , where \displaystyle t is time in years. Note: \displaystyle t=0 represents the year \displaystyle 2000 . a) When will the population reach 6000 ? b) What will the population be in \displaystyle 2030 ?

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Q7

Target-shooting disks are launched into the air from a machine \displaystyle 12 \mathrm{~m} above the ground. The height, \displaystyle h(t) , in metres, of the disk after launch is modelled by the function \displaystyle h(t)=-5 t^{2}+30 t+12 , where \displaystyle t is time in seconds.

a) When will the disk reach the ground?

b) What is the maximum height the disk reaches?

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Q8

Students at an agricultural school collected data showing the effect of different annual amounts of rainfall, \displaystyle x , in hectare-metres (ha \displaystyle \cdot \mathrm{m}) , on the yield of broccoli, \displaystyle y , in hundreds of kilograms per hectare \displaystyle (100 \mathrm{~kg} / \mathrm{ha}) . The table lists the data. a) What is an equation of the curve of good fit? b) How do you know whether the equation in part (a) is a good fit? c) Use your equation to calculate the yield when there is \displaystyle 1.85 \mathrm{ha} \cdot \mathrm{m} of annual rainfall.

\displaystyle \begin{array}{|c|c|}\hline Rainfall \mathbf{( h a} \cdot \mathbf{m}) & Yield (100 \mathrm{~kg} / \mathrm{ha}) \\ \hline 0.30 & 35 \\ \hline 0.45 & 104 \\ \hline 0.60 & 198 \\ \hline 0.75 & 287 \\ \hline 0.90 & 348 \\ \hline 1.05 & 401 \\ \hline 1.20 & 427 \\ \hline 1.35 & 442 \\ \hline 1.50 & 418 \\ \hline\end{array}

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Q9