방정식과 부등식 전체 문제

Describe the steps needed to solve a quadratic inequality graphically.

Describe the steps needed to solve a quadratic inequality algebraically.

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation

In the following exercises, determine the number of solutions for each quadratic equation.

ⓐ $9{x}^{2}-6x+1=0$ ⓑ $3{y}^{2}-8y+1=0$ ⓒ $7{m}^{2}+12m+4=0$ ⓓ $5{n}^{2}-n+1=0$

Use the Discriminant to Predict the Number of Solutions of a Quadratic Equation

In the following exercises, determine the number of solutions for each quadratic equation.

ⓐ $5{x}^{2}-7x-8=0$ ⓑ $7{x}^{2}-10x+5=0$ ⓒ $25{x}^{2}-90x+81=0$ ⓓ $15{x}^{2}-8x+4=0$

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y={x}^{2}-4x-5$

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y={x}^{2}-8x+15$

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y={x}^{2}-4x+10$

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y=-5{x}^{2}-30x-46$

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y=16{x}^{2}-8x+1$

Find the Intercepts of a Parabola

In the following exercises, find the x- and y-intercepts.

$y={x}^{2}+16x+64$

Solve Maximum and Minimum Applications

In the following exercises, find the minimum or maximum value.

$y=7{x}^{2}+14x+6$

Solve Maximum and Minimum Applications

In the following exercises, find the minimum or maximum value.

$y=-3{x}^{2}+12x-10$

A ball is thrown upward from the ground with an initial velocity of 112 ft/sec. Use the quadratic equation h = −16t² + 112t to find how long it will take the ball to reach maximum height, and then find the maximum height.

A daycare facility is enclosing a rectangular area along the side of their building for the children to play outdoors. They need to maximize the area using 180 feet of fencing on three sides of the yard. The quadratic equation $A(x)=x\left( 90-\frac{x}{2} \right)$ gives the area, A, of the yard for the length, x, of the building that will border the yard. Find the length of the building that should border the yard to maximize the area, and then find the maximum area.

Use the discriminant to determine the number and type of solutions of each quadratic equation.

$6{p}^{2}-13p+7=0$

Use the discriminant to determine the number and type of solutions of each quadratic equation.

$3{q}^{2}-10q+12=0$

A water balloon is launched upward at the rate of 86 ft/sec. Using the formula h = −16t² + 86t find how long it will take the balloon to reach the maximum height, and then find the maximum height. Round to the nearest tenth.

Solve the system by graphing: $\left\{\begin{array}{l}x-3y=-3 \\ x+y=5\end{array}\right..$

Solve the system by substitution: $\left\{\begin{array}{l}x-4y=-4 \\ -3x+4y=0\end{array}\right..$

Solve the system by elimination: $\left\{\begin{array}{l}3x-4y=-9 \\ 5x+3y=14\end{array}\right..$