Exam 9: Quadratic Equations, Inequalities, and Functions

Solve the problem, if possible. Round your answer to the nearest tenth, when appropriate. -Doris has a fish pond $15 \mathrm{ft}$ by $18 \mathrm{ft}$ . She wants to put grass in a strip of uniform width around the pond. She has enough grass seed for $234 \mathrm{ft}^{2}$ . How wide will the strip be?

Solve the inequality, and graph the solution set. - $\mathrm{s}^{2}-3 \mathrm{~s}-18<0$

Solve the inequality, and graph the solution set. - $\frac{x-4}{x+9}<0$

Choose the equation that matches the graph. -

Find the vertex of the parabola - $x=y^{2}-6 y+16$

Solve the inequality, and graph the solution set. - $\mathrm{p}^{2}+2 \mathrm{p}-3>0$

Solve by using the quadratic formula. - $8 x^{2}+7 x=-2$

Solve the problem. Round your answer to the nearest tenth, when appropriate. -A ball is thrown downward from a window in a tall building. Its position at time $t$ in seconds is given by $s(t)=16 t^{2}+32 t$ , where $s$ is in feet. How long will it take the ball to fall $160 \mathrm{ft}$ ?

Solve the equation. - $2+\frac{5}{6 z-1}=\frac{-2}{(6 z-1)^{2}}$

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - $x^{2}+8 x+7=0$

Sketch the graph of the parabola. - $\ y = -3(x +2)^2 +3$

Find the nonreal complex solutions of the equation. - $x^{2}-10 x+29=0$

Identify the vertex of the given parabola. - $f(x)=(x+2)^{2}$

Choose the one alternative that best completes the statement or answers the question. Use the quadratic formula to solve the equation. (All solutions are real numbers.) - $\frac{z^{2}}{3}=\frac{z}{2}+\frac{5}{6}$

Use the graph of a quadratic function to find the solution set of the equation or inequality. -

Determine whether a linear or quadratic function would be a more appropriate model for the graphed data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the coefficient a of $x^{2}$ should be positive or negative. -

Use the discriminant of the equation to determine the number of $x$ -intercepts. - $f(x)=-x^{2}+8 x+9$

A boy is standing on a flat field and tosses his ball toward a second boy standing at the other end of the field. The path of the ball is a parabola, and the equation of the path is $f(x)=-4 x^{2}+8 x$ . Based on this information, answer the question. -The parabola opens up.

The formula $\mathrm{A}=\mathrm{P}(1+\mathrm{r})^{2}$ gives the amount $\mathrm{A}$ in dollars that $\mathrm{P}$ dollars will grow to in 2 years at interest rate $r$ (where $r$ is given as a decimal), using compound interest. Use the formula $A=P(1+$ r) ${ }^{2}$ to find what the rate of interest is if a principal amount of $\$ 4000$ grows to $\$ 5017.60$ in 2 years, if interest is compounded annually.