Exam 9: Quadratic Equations, Inequalities, and Functions

Choose the one alternative that best completes the statement or answers the question. Use the zero factor property to solve the equation - $3 x^{2}+x-44=0$

Describe how the graph of $y=-5 x^{2}$ differs from the graph of $y=x^{2}$ .

Solve the equation by completing the square. - $3 x^{2}+8 x=-2$

Solve the equation by using the square root property or completing the square. - $4 x^{2}+16 x=64$

A manufacturer has found that the daily demand for a certain item is $\frac{500}{p}$ , where $p$ is the price of the item in dollars. The daily supply is $3 p-1$ . At what price does supply equal demand? Round your answer to the nearest cent.

Graph the parabola. - $f(x)=(x-4)^{2}+6$

Solve the inequality, and graph the solution set. - $(b+7)(b+6)(b-4)<0$

Sketch the graph of the parabola. - $y=5 x^{2}+3$

Find the term that should be added to the expression to form a perfect square trinomial. Write the resulting perfect square trinomial in factored form. - $x^{2}+5 x+$

Solve for $m$ in terms of the other variables.

Choose the one alternative that best completes the statement or answers the question. Solve the equation for the indicated variable. (Leave in your answer, when appropriate.) - $\mathrm{v}^{2}=2$ as for $\mathrm{v}$

A projectile is thrown upward so that its distance (in feet) above the ground after $t$ seconds is given by $h(t)=-12 t^{2}+456 t$ . What is its maximum height?

Choose the equation that matches the graph. -

Bob owns a watch repair shop. He has found that the cost of operating his shop is given by $c(x)=2 x^{2}-148 x+85$ , where $x$ is the number of watches repaired. How many watches must he repair to have the lowest cost?

To solve the rational inequality $\frac{-2}{x+3} \geq 2$ , you can first write the inequality with 0 on one side and the other side expressed as a single fraction. What value or values of $x$ make the denominator of that fraction equal to 0 ?

The percent increase for in-state tuition at a certain public university during the years 1991 through 1999 can be modeled by the quadratic function defined by $f(x)=0.161 x^{2}-2.09 x+10.6$ Where $x=1$ represents $1991, x=2$ represents 1992, and so on. (i) Based on this model, by what percent (to the nearest tenth) did tuition increase in 1993? (ii) In what year was the minimum tuition increase? (Round down to the nearest year.) To the nearest tenth, by what percent did tuition increase that year?

Solve the inequality, and graph the solution set. - $(c+7)(c-2)(c-5)>0$

Solve the problem. Round your answer to the nearest tenth, if necessary. -Two pipes together can fill a large tank in $10 \mathrm{hr}$ . One of the pipes, used alone, takes $15 \mathrm{hr}$ longer than the other to fill the tank. How long would each pipe take to fill the tank alone?

Solve the inequality, and graph the solution set. - $\frac{12 x}{5-x} \geq 4 x$