10.3 Quadratic Formula

10.3 Quadratic Formula

ANOTHER way to solve quadratics!

Multiple Choice

Which is the general form of a quadratic equation?

• $y=mx+b$

• $ax^2+bx+c=0$

• $\left(x-a\right)\left(x-b\right)=0$

Multiple Choice

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

We will need the general form in order to use the quadratic formula

Example

 $-x^2-4x+8=0$  

Example

 $x^2+6x=16$  

Multiple Choice

Use the quadratic formula to solve 2x² + 2x - 12?

• x = -2, 3

• x = 2, 3

• x = 2, -3

• x = -2, -3

Multiple Choice

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

•  $x=\frac{7}{2},\ x=-6$  

•  $x=-\frac{5}{2},\ x=5$  

•  $x=-\frac{3}{7},\ x=6$  

•  $x=-\frac{5}{2},\ x=7$  

Multiple Choice

Solve $2x2+7x-15=0$  

• x = -1.5 or 5

• No Solution

• x = -5 or 1.5

• x = 0.7 or 5

Example with a Complex Solution

 $2x^2-4x+5=0$  

We will use this to determine how many solutions a quadratic has!

Multiple Choice

Use the discriminant to determine the number of solutions for: $x^2-x+2=0$  

• 2 real soltuions

• 2 complex solutions

• 1 real solution

• no solution

Multiple Choice

Use the discriminant to determine the number of solutions for: $2x^2-3x-2=0$  

• 2 real solutions

• 2 complex solutions

• 1 real solution

Multiple Choice

Use the discriminant to determine the number of solutions for: $x^2-2x+1=0$  

• 2 real solutions

• 2 complex solutions

• 1 real solution

Writing a Quadratic Equation given the Solutions

Write a quadratic equation that has the solutions x = 4 and x = -7

Multiple Choice

Given the zeros , what is the quadratic equation?

• y=x² +6x -8

• y=x² +6x +8

• y=x² -2x -8

• y=x² -2x +8

Multiple Choice

Given the zeros, what is the quadratic equation?

• y=3x² +10x +8

• y=2x² ++11x +8

• y=3x² +14x +8

• y=2x² +5x +8

Multiple Choice

Write a quadratic function with solutions of

 $2+3i$  and  $2-3i$  

•  $h\left(x\right)=x^2-4x-6$  

•  $p\left(x\right)=x^2-4x-6$  

•  $k\left(x\right)=x^2-4x+13$  

•  $f\left(x\right)=x^2+4x+13$  

Poll

What is your favorite way of solving quadratic equations so far?!

• Factoring

• Square Root Property

• Completing the Square

• Quadratic Formula