Exam 8: Quadratic Equations, Functions, and Inequalities

$\log _ { 5 } 3$ is an example of a __________ inequality in one variable.

The formula is called the quadratic formula.

When we add 9 to $x ^ { 2 } + 6 x$ , we say that we have completed the _________.

Use completing the square to solve the equation. $6 x ^ { 2 } - 5 x - 2 = 0$

Solve $\frac { x ^ { 2 } } { 4 } + \frac { x } { 5 } = \frac { 1 } { 20 }$ by any method.

Solve: $3 x ^ { 2 } - x - 2 > 0$

Graph the inequality. $\log _ { 5 } 3$

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

$x ^ { 2 } + 3 x - 17 < 0$ is an example of a quadratic __________ in one variable.

Solve by the quadratic formula: $x ^ { 2 } = 4 x - 2$

Solve the equation. $x ^ { 2 } + 10 x + 18 = 0$

Find the vertex for $f ( x ) = - x ^ { 2 } - 4 x + 3$ .

Solve: $\frac { x - 9 } { x + 2 } < 0$

What are the critical numbers for each inequality? a. $x ^ { 2 } - 4 x - 21 \geq 0$ __________ b. $\frac { x - 3 } { x ( x + 3 ) } > 0$ __________

Solve the equation. $3 x ^ { 2 } - 4 x + 2 = 0$

Refer to the graph. Fill in the blank. The lowest point on the graph is (1,-1) . This is called the __________ of the parabola.

Give the vertex of $f ( x ) = \frac { 1 } { 8 } ( x - 9 ) ^ { 2 } + 3$ .

Use the quadratic formula to solve the equation. $0.2 x ^ { 2 } - 0.16 x - 0.1 = 0$

Solve the inequality. Write the solution set in interval notation and graph it. $\log _ { 5 } 3$

Determine a quadratic function whose graph has x -intercepts of (-1,0) and (3,0) .