2-14 quadratic formula

Determine the values of a, b, and c for the quadratic equation:

4x² – 8x = 3

• a = 4, b = -8, c = 3

• a = 4, b =-8, c =-3

• a = 4, b = 8, c = 3

• a = 4, b = 8, c = -3

Use the quadratic formula to find the solutions for

y = -x² - 5x + 12

• No Real Solution

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Solve using the quadratic formula.
2x² - 9x - 35 = 0

• x = 7/2, x = -6
• x = -5/2, x =5
• x = -3/7, x =6
• x = -5/2, x = 7

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.

 $m^2=-10m+15$  

•  $\left\{-5+\sqrt{10},-5-\sqrt{10}\right\}$  

•  $\left\{5+2\sqrt{10},\ 5-2\sqrt{10}\right\}$  

•  $\left\{-5+2\sqrt{10},-5-2\sqrt{10}\right\}$  

•  $\left\{\frac{-10+\sqrt{115}}{2},\frac{-10-\sqrt{115}}{2}\right\}$  

 $4b^2=4$  

•  $\left\{i,\ -i\right\}$  

•  $\left\{4+2\sqrt{6},\ 4-2\sqrt{6}\right\}$  

•  $\left\{1,\ -1\right\}$  

•  $\left\{\frac{4+2\sqrt{22}}{9},\frac{4-2\sqrt{22}}{9}\right\}$  

 $7k^2-k=11$  

•  $\left\{\frac{1+\sqrt{78}}{14},\frac{1-\sqrt{78}}{14}\right\}$  

•  $\left\{\frac{1+\sqrt{309}}{14},\frac{1-\sqrt{309}}{14}\right\}$  

•  $\left\{\frac{-1+3\sqrt{5}}{2},\frac{-1-3\sqrt{5}}{2}\right\}$  

•  $\left\{\frac{-1+i\sqrt{307}}{14},\frac{-1-i\sqrt{307}}{14}\right\}$  

 $-8a^2-6a-4=1$  

•  $\left\{\frac{3-i\sqrt{31}}{8},\frac{3+i\sqrt{31}}{8}\right\}$  

•  $\left\{\frac{-1+\sqrt{6}}{3},\frac{-1-\sqrt{6}}{3}\right\}$  

•  $\left\{-3+\sqrt{14},-3-\sqrt{14}\right\}$  

•  $\left\{\frac{-3-i\sqrt{31}}{8},\frac{-3+i\sqrt{31}}{8}\right\}$  

 $14n^2-15=5n^2+2$  

•  $\left\{\frac{\sqrt{17}}{3},\frac{-\sqrt{17}}{3}\right\}$  

•  $\left\{\frac{\sqrt{17}}{6},\frac{-\sqrt{17}}{6}\right\}$  

•  $\left\{\frac{5+i\sqrt{7}}{2},\frac{5-i\sqrt{7}}{2}\right\}$  

•  $\left\{\frac{-5+i\sqrt{199}}{14},\frac{-5-i\sqrt{199}}{14}\right\}$  

 $-4k^2-10=\ -5$  

•  $\left\{-\frac{i\sqrt{5}}{2},\frac{i\sqrt{5}}{2}\right\}$  

•  $\left\{\sqrt{5},-\sqrt{5}\right\}$  

•  $\left\{-\frac{i\sqrt{5}}{4},\frac{i\sqrt{5}}{4}\right\}$  

•  $\left\{\frac{5-i\sqrt{15}}{20},\frac{5+i\sqrt{15}}{20}\right\}$