Write in standard form.
a) \displaystyle f(x)=(3 x-5)(2 x-9) \quad b) \displaystyle f(x)=(6-5 x)(x+2)
Write in factored form.
\displaystyle f(x)=x^{2}-81
Write in factored form.
\displaystyle f(x)=6 x^{2}+5 x-4
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
Can all quadratic equations be solved by factoring? Explain.
Solve by graphing.
\displaystyle x^{2}+6 x-3=-3
Solve by graphing.
\displaystyle 2 x^{2}-5 x=7
Solve by factoring.
\displaystyle 2 x^{2}+11 x-6=0
Solve by factoring.
\displaystyle x^{2}=4 x+21
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 ?
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?
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}