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Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$4{d}^{2}-7d+2=0$

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$\frac{3}{4}{b}^{2}+\frac{1}{2}b=\frac{3}{8}$

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$\frac{1}{9}{c}^{2}+\frac{2}{3}c=3$

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$2{x}^{2}+12x-3=0$

Solve Quadratic Equations Using the Quadratic Formula

In the following exercises, solve by using the Quadratic Formula.

$16{y}^{2}+8y+1=0$

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

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

• ⓐ $4{x}^{2}-5x+16=0$
• ⓑ $36{y}^{2}+36y+9=0$
• ⓒ $6{m}^{2}+3m-5=0$
• ⓓ $18{n}^{2}-7n+3=0$

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

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

• ⓐ $9{v}^{2}-15v+25=0$
• ⓑ $100{w}^{2}+60w+9=0$
• ⓒ $5{c}^{2}+7c-10=0$
• ⓓ $15{d}^{2}-4d+8=0$

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

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

• ⓐ ${r}^{2}+12r+36=0$
• ⓑ $8{t}^{2}-11t+5=0$
• ⓒ $4{u}^{2}-12u+9=0$
• ⓓ $3{v}^{2}-5v-1=0$

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

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

• ⓐ $25{p}^{2}+10p+1=0$
• ⓑ $7{q}^{2}-3q-6=0$
• ⓒ $7{y}^{2}+2y+8=0$
• ⓓ $25{z}^{2}-60z+36=0$

Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

ⓐ ${x}^{2}-5x-24=0$ ⓑ ${(y+5)}^{2}=12$ ⓒ $14{m}^{2}+3m=11$

Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

ⓐ ${(8v+3)}^{2}=81$ ⓑ ${w}^{2}-9w-22=0$ ⓒ $4{n}^{2}-10=6$

Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

ⓐ $6{a}^{2}+14=20$ ⓑ ${\left(x-\frac{1}{4}\right)}^{2}=\frac{5}{16}$ ⓒ ${y}^{2}-2y=8$

Identify the Most Appropriate Method to Use to Solve a Quadratic Equation

In the following exercises, identify the most appropriate method (Factoring, Square Root, or Quadratic Formula) to use to solve each quadratic equation. Do not solve.

ⓐ $8{b}^{2}+15b=4$ ⓑ $\frac{5}{9}{v}^{2}-\frac{2}{3}v=1$ ⓒ ${\left(w+\frac{4}{3}\right)}^{2}=\frac{2}{9}$

A flare is fired straight up from a ship at sea. Solve the equation $16({t}^{2}-13t+40)=0$ for $t$, the number of seconds it will take for the flare to be at an altitude of 640 feet.

An architect is designing a hotel lobby. She wants to have a triangular window looking out to an atrium, with the width of the window 6 feet more than the height. Due to energy restrictions, the area of the window must be 140 square feet. Solve the equation $\frac{1}{2}{h}^{2}+3h=140$ for $h$, the height of the window.

Solve the equation ${x}^{2}+10x=200$ ⓐ by completing the square ⓑ using the Quadratic Formula ⓒ Which method do you prefer? Why?

Solve the equation $12{y}^{2}+23y=24$ ⓐ by completing the square ⓑ using the Quadratic Formula ⓒ Which method do you prefer? Why?

The sum of two consecutive odd numbers is $-100$. Find the numbers.

The area of triangular mural is 64 square feet. The base is 16 feet. Find the height.

Find the length of the hypotenuse of a right triangle with legs 5 inches and 12 inches.