Solving Quadratic Equations

Solving Quadratic Equations

Math 9

Solving Quadratic Equations

Extracting Square Roots

Factoring

Completing the Square

Quadratic Formula

An equation in which the highest power of the variable is 2.

Quadratic Equation

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

Multiple Select

Choose what are the examples of quadratic equations in the following:

• $a^2+2a-4$

• $2x+2x-6$

• $y^3-2y^2+1=0$

• $2b^2-4b+5$

Extracting Square Roots

• Square root both sides

• Affix

   $\pm$  (positive and negative signs)

Multiple Choice

Solve for x using extracting square roots

 $n^2=39$  

•  $\pm9\sqrt{30}$  

•  $\pm\sqrt{39}$  

•  $\pm39$  

Multiple Choice

Solve for x using extracting square roots:

 $\frac{16}{25}=u^2$  

•  $\sqrt{\frac{4}{5}}$  

•  $\pm\frac{4}{5}$  

•  $\pm\sqrt{\frac{4}{5}}$  

Multiple Choice

Solve for x using extracting square roots

 $3r^2=40$  

•  $\pm2\sqrt{\frac{10}{3}}$  

•  $\pm\sqrt{\frac{40}{3}}$  

•  $2\sqrt{\frac{40}{3}}$  

Multiple Choice

Solve the quadratic equation: $4x^2–7=9$  

•  $\pm2$  

•  $\pm4$  

•  $\pm6$  

•  $\pm8$  

Multiple Choice

Solve the quadratic equation.

(x + 4)(x + 1) = 0

• x = 4 or x = 1

• x = -4 or x = 1

• x = -4 or x = -1

• x = 4 or x = -1

Multiple Choice

Solve the quadratic equation by factoring: $4⁢x^2−20⁢x+28=3$  

•  $x=5$  

•  $x\ =\ \frac{5}{2}$  

•  $x\ =\ \frac{2}{5}$  

•  $x\ =\ -\frac{5}{2}$  

Factoring

• Look at the first and last terms

• Find two numbers which, when multiplied will give the last term.

• Test if the sum of those two numbers will give you the middle term.

Multiple Choice

What are the factors of a quadratic equation

 $p^2+3p-4\ =\ 0$  

•  $\left(p+4\right)\left(p-1\right)$  

•  $\left(p-4\right)\left(p+1\right)$  

•  $\left(p+2\right)\left(p-2\right)$  

Multiple Choice

Solve this quadratic equation: $x^2-7x+10\ =\ 0$  

•  $x=2;\ x=5$  

•  $x\ =-2;\ x=-5$  

•  $x=-2;\ x=5$  

•  $x=2;\ x=-5$  

Multiple Choice

What are the values of x in the quadratic equation

 $x^2-2x+1$  using factoring?

•  $x\ =\ 1$  

•  $x=1;\ x\ =-1$  

•  $x=-1$  

Multiple Choice

Solve by factoring: x² = 7x + 18

• -7 and -18

• 9 and 2

• 9 and -2

• 2 and 7

Multiple Choice

 $x^2+2x-3\ =\ 0$  

What are the values of x in this quadratic equation?

•  $x=1,\ x\ =-3$  

•  $x\ =\ 0,\ x\ =-2$  

•  $x=1,\ x=2$  

Multiple Choice

What should you do first in solving this equation?

x² + 6x - 13 = 3

• Get factored form

• Write down: a=1, b=6, c=-13

• Make it equal 0 by subtracting 3 on each side

• Equate the factors to 0

Multiple Choice

Solve by factoring:

x² + 4x - 40 = -8

• -10 & -4

• -4 & 10

• -8 & 4

• 8 & -4

Completing the Square

• Move all the constant to another side

• Add

   $\left(\frac{b}{2}\right)^2$  to both sides

• Factor and Solve

Multiple Choice

What is the first step to solving THIS equation by completing the square?

a² + 10a + 21 = 0

• Set the equation equal to zero

• Divide 10 by 2 and add the result to both sides

• Add a² and 10a together

• Subtract 21 on both sides

Multiple Choice

Complete the square.
x² + 14x + ____

• x² + 14x - 196
• x² + 14x + 49
• x² + 14x - 49
• x² + 14x + 196

Multiple Choice

Complete the Square

x² + 10x + ____

• x² + 10x - 100

• x² + 10x + 100

• x² + 10x - 25

• x² + 10x + 25

Multiple Choice

Complete the square for

x² + 12x + ____

• x² + 12x + 144

• x² + 12x + 36

• x² + 12x - 36

• x² + +12x - 144

Multiple Choice

What are the roots of this quadratic equation

 $x^2+12x+32\ =\ 0$  using the completing the square?

•  $x=-4;\ x=-8$  

•  $x=4;\ x=-8$  

•  $x=4;\ x=8$  

Multiple Choice

Solve the following quadratics equation by completing the square...

x² + 4x + 1 = 0

• x = -2 ± √3

• x = -3 ± √2

• x = 2 ± √3

• x = 2 ± √2

Quadratic Formula

• Get the values of a, b and c

• Substitute to the formula

• Factor and Solve.

Multiple Choice

Solve Using the Quadratic Formula

x² + 4x - 32 = 0

• -10 & -4

• -4 & 10

• -8 & 4

• 8 & -4

Multiple Choice

Solve the following for x by using the Quadratic Formula

 $2x^2\ +6x\ -\ 7\ =\ 0$