Solving Quadratic Equations

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
• Type it all in a calculator.

What is this formula?

• This is the speed of light formula.
• This is the quadratic formula.
• This is the zero product property.
• This is scary.

Solve Using the Quadratic Formula
 x² + 4x - 40 = -8

• -10 & -4
• -4 & 10
• -8 & 4
• 8 & -4

Which is the standard form for a quadratic equation?

• $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

• $ax^2+bx+c=0$

• $y=a\left(x-h\right)^2+k$

• $a^2+b^2=c^2$

Which is in the proper factored form to use the Zero Product Property ?

• $x^2-x=12$

• $x\left(x-1\right)=12$

• $\left(x-4\right)\left(x+3\right)=1$

• $\left(x-4\right)\left(x+3\right)=0$

 $7x^2=6x-1$  

Given this quadratic equation, what could be the values a, b, and c to use in the quadratic formula?

•  $a\ =\ 7,\ b\ =\ -6,\ c\ =\ 1$  

•  $a\ =\ 1,\ b\ =\ 6,\ c\ =\ -7$  

•  $a\ =\ -7,\ b\ =\ 6,\ c\ =\ 1$  

•  $a\ =\ 6,\ b\ =\ 7,\ c\ =\ 1$  

 $x^2-7x=0$  

Solve by the method of your choice.

• x = 7 only
  

• x = 0 only
  

• x = 0 and 7
  

• There is no real answer for this equation.
  

 $3x^2-10x+1=0$  

Solve by the method of your choice.

•  $x=\frac{-10\pm\sqrt{88}}{6}$  

•  $x=\frac{-5\pm2\sqrt{22}}{3}$  

•  $x=\frac{10\pm\sqrt{112}}{6}$  

•  $x=\frac{5\pm\sqrt{22}}{3}$  
  

What is the color of the graph that has exactly one real zero?

• black

• green

• purple

• red

• None of these graphs has exactly one zero.

How many real solutions can a quadratic equation of the form shown have?
Check all that apply.

 $ax^2+bx+c=0$  

• 0

• 1

• 2

• 3

• infinitely many