Exam 8: Quadratic Equations and Functions

Solve. -A developer wants to enclose a rectangular grassy lot that borders a city street for parking. If the developer has 308 feet of fencing and does not fence the side along the street, what is the largest area that can be enclosed?

Solve. -Because of the increase in traffic between Springfield and Orangeville, a new road was built to connect the two towns. The old road goes south $x$ miles from Springfield to Freeport and then goes east $x + 3$ miles from Freeport to Orangeville. The new road is 9 miles long and goes straight from Springfield to Orangeville. Find the number of miles that a person saves by driving the new road over the old one.

Solve. - $x ^ { 4 } - 16 = 0$

Use the discriminant to determine the number and type of solutions of the equation. - $25 x ^ { 2 } - 10 x + 1 = 0$

Use the quadratic formula to solve the equation. - $\frac { z ^ { 2 } } { 2 } = \frac { z } { 7 } + \frac { 9 } { 14 }$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 5 x + 4 > 0$

Match the function with its graph. - $f ( x ) = x ^ { 2 } + 4 x$

Use the square root property to solve the equation. $x ^ { 2 } = 120$

Solve. - $2 + \frac { 5 } { 7 x - 1 } = - \frac { 2 } { ( 7 x - 1 ) ^ { 2 } }$

Solve the inequality. Write the solution set in interval notation. - $\frac { - 6 } { - 3 x - 4 } > 0$

Solve. -The revenue for a small company is given by the quadratic function $r ( t ) = 6 t ^ { 2 } + 4 t + 550$ where $t$ is the number of years since 2010 and $r ( t )$ is in thousands of dollars. If this trend continues, find the year after 2010 in which the company's revenue will be $\$ 872$ thousand. Round to the nearest whole year.

Solve. - $x ^ { 2 / 3 } - 7 x ^ { 1 / 3 } + 12 = 0$

Solve the inequality. Write the solution set in interval notation. - $( x + 5 ) ( x - 5 ) > 0$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = - 4 ( x - 3 ) ^ { 2 } + 6$

Solve. - $\frac { 1 } { x } + \frac { 1 } { x - 3 } = \frac { x - 2 } { x - 3 }$

Solve the equation. - $y ^ { 2 } - 3 y = 2$

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

Solve the equation by completing the square. - $2 x ^ { 2 } + 12 x + 3 = 0$

Use the quadratic formula to solve the equation. - $16 \mathrm { x } ^ { 2 } + 1 = 5 \mathrm { x }$

Sketch the graph of the quadratic function. Give the vertex and axis of symmetry. - $f ( x ) = - x ^ { 2 } - 1$