Solving Quadratic Equations

Solving Quadratic Equations

Extracting Square Roots

Factoring

Completing the Square

Quadratic Formula

Open Ended

Based on the figure below, what is a quadratic equation?

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:

 $\frac{16}{125}=u^2$  

•  $\sqrt{\frac{4}{5}}$  

•  $\pm\frac{4}{5}$  

•  $\pm\sqrt{\frac{4}{5}}$  

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 for x using extracting square roots

 $n^2=39$  

•  $\pm9\sqrt{30}$  

•  $\pm\sqrt{39}$  

•  $\pm39$  

Factoring

• Look at the first and last terms

• Find two numbers that if you multiply will gives the last term.

• Test if you add them will give you the middle term.

Multiple Choice

What are the factors of a quadratic equation

 $p^2+3p-4$  

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

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

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

Multiple Choice

What are the factors of quadratic equation

 $2y^2+7y+3$  

•  $\left(2y+3\right)\left(y+1\right)$  

•  $\left(2y+7\right)\left(y-1\right)$  

•  $\left(2y+1\right)\left(y+3\right)$  

Multiple Choice

What are the values of x in the quadratic equation

 $x^2-2x+1$  using factoring?

•  $x\ =\ 1;\ x\ =\ 1$  

•  $x=1;\ x\ =-1$  

•  $x=-1;\ x=-1$  

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 are the roots of this quadratic equation

 $r^2+12r+32$  using the completing the square?

•  $x=-4;\ x=-8$  

•  $x=4;\ x=-8$  

•  $x=4;\ x=8$  

Multiple Choice

Give the number must be added to the both sides to complete the square.

 $t^2+4t+$  ____ $=5+$ ___

• 2

• 3

• 4

Multiple Choice

 $x^2+8x-20=0$  , what are the roots of this quadratic equation?

•  $x=2;\ x=-10$  

•  $x=-2;\ x=10$  

•  $x\ =-2;\ x=-10$  

Quadratic Formula

• Get the values of a, b and c

• Substitute to the formula

• Factor and Solve.

Quadratic Formula

• Get the values of a, b and c

• Substitute to the formula

• Factor and Solve.

Multiple Choice

 $x^2+2x-3$  

What are the values in this quadratic equation

•  $a=1,\ b=2,\ c\ =-3$  

•  $a\ =\ 0,\ b\ =-2,\ c=-3$  

•  $a=1,\ b=2,\ c=3$  

Multiple Choice

 $y^2+7y+10$  

, what are the roots of this quadratic equation?

•  $x=2;\ x=-5$  

•  $x\ =-2;\ x=-5$  

•  $x=-2;\ x=5$  

Open Ended

What did you learn this day?