이차방정식의 판별식과 근과 계수의 관계

Solve Quadratic Equations Using the Quadratic Formula

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

$25{q}^{2}+30q+9=0$

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 Real Solutions of a Quadratic Equation

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

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

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

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

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

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

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

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

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

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

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

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.

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

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.

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

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.

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

Solve the equation ${x}^{2}+10x=120$

ⓐ 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?

How do we recognize when an equation is quadratic?

When we solve a quadratic equation, how many solutions should we always start out seeking? Explain why when solving a quadratic equation in the form $a{x}^{2}+bx+c=0$ we may graph the equation $y=a{x}^{2}+bx+c$ and have no zeroes (x-intercepts).

When we solve a quadratic equation by factoring, why do we move all terms to one side, having zero on the other side?

In the quadratic formula, what is the name of the expression under the radical sign ${b}^{2}-4ac,$ and how does it determine the number of and nature of our solutions?

Describe two scenarios where using the square root property to solve a quadratic equation would be the most efficient method.

For the following exercises, solve the quadratic equation by factoring.

${x}^{2}+4x-21=0$

For the following exercises, solve the quadratic equation by factoring.

${x}^{2}-9x+18=0$

For the following exercises, solve the quadratic equation by factoring.

$2{x}^{2}+9x-5=0$