Method 1
Use the Zero Product Property to solve the following quadratic equation. (x - 7)(x + 2) = 0
x = 7 x = -2
Factor completely: 6x+9
3(2x+3)
Solve for x. x2+5x+6=0
x= -2, x= -3
Factor completely:x3+2x2+3x+6
(x+2)(x2+3)
What is the Discriminant of x2+5x+6=0
1
Solve the following quadratic equation.
x2+3x+2 = 0
x = -2 x = -1
Factor completely: 12x2−8x
4x(3x-2)
Solve for x. 2x2−7x+3=0
x = 3, x = 1/2
Factor completely: 2x3−5x2+6x−15
(2x−5)(x2+3)
What are the three different types of solutions we can have when solving quadratics?
No real solution (Imaginary), One solution or Two solutions
Solve the following quadratic equation.
x2 - 6x + 5 = 0
x = 5 x = 1
Factor Completely.15a3b2+10a2b3-5ab
5ab(3a2b+2ab2−1)
Solve for x.
x2−6x+9=0
x =3 , x=3
Factor completely: 4a2b+6ab+2a+3
(2a+3)(2ab+1)
How do we know a quadratic function does not have solutions when looking at a graph?
It does not touch or pass through the x-axis
Solve the following quadratic equation.
x2 - 6x - 27 = 0
x = 9 x = -3
Factor completely: 2x3+10x2+12x
2x(x+2)(x+3)
Solve using the quadratic formula: x2+2x+5=0
No Real Solutions
Factor completely: 3x4+6x3+9x2+18x
3x(x+2)(x2+3)
What is the discriminant of 2x2−7x+3=0
DAILY DOUBLE: What does this mean about the solutions?
25
Solve the following quadratic equation.
x2-16x+64 = 0
x = -8, x= -8
Factor completely: 3a3b−12ab3
3ab(a+2b)(a−2b)
Solve for x.
3x2−5x−1=0
x=(5+-sqrt37)/6
Factor completely: 5a3b+10a2b2+3a2+6ab
a(a+2b)(5ab+3)
How do we know how many solutions a quadratic function will have when using the quadratic formula?
Look at the discriminant [b^2-(4ac)] (i.e. the number under the square root)
d>0....Two Solutions
d=0....One Solution
d<0....No real solution