Exam 8: Quadratic Equations, Functions, and Inequalities

The revenue R (in dollars)for selling x units of an infant stroller is modelled by $R = x \left( 50 - \frac { 1 } { 4 } x \right) , 0 < x < 100$ . Find the number of strollers that must be sold to produce a revenue of $2176 . Round your answer to the nearest integer.

Use the Quadratic Formula to solve $0.09 s ^ { 2 } - 0.12 s + 0.04 = 0$ . Round your answer(s)to two decimal places.

Your home is on a square lot. To add more space to your yard, you purchase an additional 30 feet along the side of your property (see figure). The area of the lot is now 43,875 square feet. What are the dimensions of the new lot?

You are investing $\$ 1000$ in a certificate of deposit for 2 years and you want the interest for that time to exceed $\$ 50$ . The interest is compounded annually. What interest rate should you have? Hint: Solve the inequality $1000 ( 1 + r ) ^ { 2 } > 1,050$ . Round your answer to one decimal place.

If the perimeter of a rectangle is 75 meters, and the length is 1.5 times the width, find the area of the rectangle in square meters. Round your answer to two decimal places.

Use a graphing calculator to approximate the values of x that satisfy the inequality $x ^ { 2 } - 3 x + 3 \leq 57$ .

Write the quadratic equation having solutions $- 4 + \sqrt { 5 } , - 4 - \sqrt { 5 }$

Find all real and complex solutions of the quadratic equation $( x + 7 ) ^ { 2 } + 28 = 0$ .

The amount A in an account earning r percent (in decimal form)compounded annually for two years is given by $A = P ( 1 + r ) ^ { 2 }$ where P is the original investment. What is the interest rate r , as a percent, if the amount in the account is $235.44 and the original investment was $208 ? Round your answer to two decimal places.

Graph the solution to the inequality on the real number line. $4 x ( 3 - x ) \geq 0$

Solve the equation $x ^ { 1 / 3 } - 2 x ^ { 1 / 6 } - 24 = 0$ . (Find all real and complex solutions.)

Find the vertex of $y = 6 x ^ { 2 } + 12 x - 6$ .

Graph the solution to the inequality on the real line. $\frac { x + 4 } { 3 x + 3 } \leq 0$

Solve the equation $x ^ { 2 / 3 } - 2 x ^ { 1 / 3 } - 63 = 0$ . (Find all real and complex solutions.)

Solve the equation $8 ( 6 - x ) - 3 x ( 6 - x ) = 0$ by factoring.

What term should be added to $t ^ { 2 } + 11 t$ to make it a perfect square trinomial?

Find the intercepts of $y = 2 x - x ^ { 2 }$ .

Write the quadratic equation having solutions $4 i , - 4 i$

Graph the solution to the inequality on the real number line. $4 x ^ { 2 } + 20 x + 25 \leq 0$

Find the vertex of the graph of the function $y = 9 x ^ { 2 } + 6 x + 4$ by using the formula $x = - b / ( 2 a )$ .