Solving Quadratic Equations

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 ?

• $x^2-x=12$

• $x\left(x-1\right)=12$

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

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

Given this graph is the function of

 $y=x^2-2x-8$  , what is the solution to  $x^2=2x+8$  ?

• (1, 9)
  

• x = {-2, 4}
  

• (0, 8)
  

• x = {5, 2}
  

 $7x^2=6x-1$  

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.
  

 $2x^2=8x+3$ 

 

 $2x^2-8x-3=0$  

 $x=\frac{8\pm\sqrt{64-4\left(2\right)\left(-3\right)}}{4}$  

 $x=\frac{8\pm\sqrt{40}}{4}$ 

 $x=\frac{8\pm2\sqrt{10}}{4}$  

 $x=\frac{4\pm\sqrt{10}}{2}$  

Suzanne solved the equation using this process.

Did she make a mistake?

If yes, at which line did she make her first mistake?

(There are 5 steps in her process)

• Suzanne made no errors.
  

• Step 2
  

• Step 3
  

• Step 4
  

• Step 5
  

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.

9k² = 225

• 4
• 4, -4
• 25, -25
• -5, 5

Factor x²-2x-15

• (x+5)(x-3)
• (x-5)(x-3)
• (x-5)(x+3)
• (x+5)(x+3)

Factor:
p² - 14p

• p(1 - 14)
• 2p(p - 7)
• p²(1-14)
• p(p - 14)