Quadratic Formula

Quadratic Formula

Please write the formula!!!!

Multiple Select

What are some other names for "solutions to a quadratic equation?" Check all that apply.

• Roots

• y-intercepts

• Zeros

• x-intercepts

Multiple Select

How many "real" solutions can there be for a quadratic equation? Check all that apply.

• Zero

• One

• Two

• Infinitely many

Open Ended

What does it mean to be a solution to a quadratic equation?

Multiple Select

What are the solution(s) to  $x^2+4x+3=0$ 

Check all that apply.

• 0
  

• -1

• 1

• -3

• No "real" solution

 $x^2+4x+3=0$  

• a=1, b=4, c=3

•  $\frac{-\left(4\right)\pm\sqrt{\left(4\right)^2-4\left(1\right)\left(3\right)}}{2\left(1\right)}$  

•  $\frac{-4\pm\sqrt{16-12}}{2}$  

•  $\frac{-4\pm\sqrt{4}}{2}=\frac{-4\pm2}{2}$  

•  $\frac{-4+2}{2}=-1\ \ \ OR\ \ \ \frac{-4-2}{2}=-3$  

Multiple Select

Please find the roots to   $-2x^2-8x-10=0$ 

Check all that apply.

• 0

• -1
  

• -3

• 3

• No "real" solution

 $-2x^2-8x-10=0$  

• a=-2, b=-8, c=-10

•  $\frac{-\left(-8\right)\pm\sqrt{\left(-8\right)^2-4\left(-2\right)\left(-10\right)}}{2\left(-2\right)}$  

•  $\frac{8\pm\sqrt{64-80}}{-4}$  

•  $\frac{8\pm\sqrt{-16}}{-4}=\frac{8\pm4i}{-4}$  Don't worry! I'll teach this soon.  It means no "REAL" solutions

•  $-2+i\ \ \ OR\ \ -2-i$  

Multiple Choice

What is the discriminant of the equation $3x^2-6x+7=0$ 

• -48

• 120

• 84

 $3x^2-6x+7=0$  

• a=3, b=-6, c=7

• plug into  $b^2-4ac$  

•  $\left(-6\right)^2-4\left(3\right)\left(7\right)=36-84=-48$  

Multiple Choice

What is the discriminant of  $x^2-9=0$  

• 6

• 60

• -36

• 36

 $x^2-9=0$  

• a=1, b=0, c=-9

• plug into  $b^2-4ac$  

•  $\left(0\right)^2-4\left(1\right)\left(-9\right)=0+36=36$  

Open Ended

What is the discriminant of the equation $4x^2+12x+9=0$ 

 $4x^2+12x+9=0$  

• a=4, b=12, c=9

• plug into  $b^2-4ac$  

•  $\left(12\right)^2-4\left(4\right)\left(9\right)=144-144=0$  

Multiple Choice

Which graph shows a negative discriminant?

• Red

• Blue

• Yellow

Multiple Choice

Which graph shows a positive discriminant?

• Red

• Blue

• Yellow

Multiple Choice

Which graph shows a discriminant = 0?

• Red

• Blue

• Yellow

Open Ended

How many "real" solutions are shown in graph A?

Open Ended

Which graph shows 2 "real" solutions?

Open Ended

Graph B shows one real solution. What is its discriminant?