SQUARE ROOT METHOD
True or False: The square root of a number is both positive and negative.
Example:
sqrt36 = pm6
True
When completing the square, what formula do you use to determine which number you need to add to both sides?
(b/2)^2
What is the quadratic formula?
(-bpmsqrt(b^2 - 4ac) )/ (2a)
What formula would you use to find the number of solutions of a quadratic equation AKA the discriminant?
b^2-4ac
Using the square root method, solve the following quadratic equation.
x^2 + 13 = 62
x = pm7
What value do you need to add to both sides in order to complete the square?
x^2 + 12x = 3
36
Identify the a, b, and c of the quadratic equation.
12 + 3x^2 -5x=0
a=3
b=-5
c=12
What is the discriminant of the following quadratic formula and how many solutions does it have?
3x^2 + 7x -4
97 ; two solutions
Using the square root method, solve the following quadratic equation.
(x - 5)^2 = 81
x = 5pm9
x = 14 and x = -4
What does the following equation look like AFTER it's been factored?
x^2 +14x +49 = 64
(x + 7)^2 = 64
Solve the quadratic equation by using the quadratic formula.
5x^2 + 6x-2=0
x= (-6pmsqrt(36-(-40)))/10
x= (-6pmsqrt(76))/10
What is the discriminant of the following quadratic formula and how many solutions does it have?
x^2 +5x + 10
-15 ; no solutions
Using the square root method, solve the following quadratic equation.
3x^2 +19 = 28
x=pmsqrt3
Solve the following quadratic equation by completing the square.
x^2 +18x +3=22
x = -9pmsqrt100
x=-9pm10
Solve the quadratic equation by using the quadratic formula.
4x^2-4x+1=0
x= (4pmsqrt(16-16))/8
x= (4pmsqrt(0))/8
What is the discriminant of the following quadratic formula and how many solutions does it have?
3x^2 + 3 = -6x
0 ; one solution
Using the square root method, solve the following quadratic equation.
(2x-8)^2 = 100
x = (8pmsqrt100)/2
x = (8pm100)/2
Solve the following quadratic equation by completing the square.
x^2+6x+4=0
x=-3pmsqrt5
Solve the quadratic equation by using the quadratic formula.
x^2 +3=-4x
x = (-4pmsqrt(16-12))/2
x = (-4pmsqrt(4))/2
What is the discriminant of the following quadratic formula and how many solutions does it have?
x^2 +9x = -10
41 ; two solutions