Factoring
x2 - 1 = 0
{-1, 1}
Solve the following quadratic equation by factoring:
x2 - 4 = 0
Difference of squares
(x +2)(x - 2)
x = {-2, 2}
What number completes the square?
x2 - 9x + ______
81/4
Solve with square roots
x^2+4=20
x=-4 and x=4
Convert the quadratic equation to standard form, factored form and graph.
f(x) -(x -7)2+ 1
standard Form: f(x) = -(x2-14x + 49) + 1 f(x) = -x2+ 14x -49 + 1
standard Form: f(x) = -x2+ 14x -48
Factored Form: f(x) = -1(x2 -14x + 48)
Factored Form: f(x) = -1(x - 6)(x - 8) x = {6, 8}Graph: reflected over x axis, vertex (7, 1) roots (6,8)
Solve the following quadratic equation by factoring.
x2 + 12x + 27 = 0
find factors of 27 that sum 12
x + 9)(x + 3)
x + 9 = 0 and x + 3 = 0
x = -9 and x = -3
x = {-9, -3}
Solve the following quadratic equation by factoring:
9x2 - 81x = 0
GCF 9x(x - 9)
x = {0, 9}
What is the solution to the following equation in simplest form?
x2 = 24
x = +/-2 Sq Rt of 6
Solve with square roots:
4x^2+2=18
x=2 or x=-2
Convert the quadratic Equation to vertex formula, factored form and graph
f(x) =x2 + 10x + 21
V Fm: f (x) = (x2+ 10x + ) + 21
52 = 25
f (x) = (x2+ 10x + 25) + 21 - 25
f (x) =(x + 5)2 - 4 V:(-5, -4) Axis = -5
Factored Form (x + 7)(x + 3) x = { -7, -3}
Solve the following quadratic equation by factoring.
2x2 + 6x - 80 =0
2(x2+ 3x - 40) Find factors of -40 that sum 3
2(x + 8)(x - 5)
x + 8 = 0 and x - 5 = 0
x = -8 and x = 5
x = {-8, 5}
Solve the following quadratic equation by factoring:
2a2b - 32a4b
GCF 2a2b (1 - 16a2)
Difference of Squares: 2a2b (1 - 4a)(1 + 4a)
Solve the following quadratic equation by completing the square: f(x) = x2 - 2x = 24
f(x) = (x2 - 2x + ) - 24 = 0 Note: find (b/2)2
(-2/2)2 = 1 f(x) = (x2 - 2x + 1) - 24 - 1
= (x - 1)2 = 25
x -1 = 5 and x = 1 +/- 5
x = {-4, 6}
Solve with square roots:
6x^2-12=138
x=5 and x=-5
Find the Roots/Solutions by Graphing
x2 - 8x + 16
x = -b/2a - - 8/2 = 4
x | y x = {4}
2 | 4 3 | 1 4 | 0
Solve the following quadratic equation by factoring.
b2 - 8b = 20
{10, -2}
Solve the following quadratic equation by factoring:
5n2 + 41n - 12 = -4 + 2n
5n2+ 39n - 8 = 0
n2 + 39n - 40 Find Product of -40 that sums 39 : 40 & -1 Divide both by 5: (x + 8)(5x - 1)
x = {1/5, -8}
Solve the following quadratic equation by completing the square: x2 + 10x +5 = 0
x2 + 10x +5 = 0
(x + 5)2= -5 + 25 = 20
(x + 5)2= 20..x + 5=(sqrt4)(sqrt5)
-5 +- 2(sqrt5)
Solve using square root method:
(y - 4)2 = 121
y - 4 = +/- square root 121
y = 4 + 11 and y = 4 - 11
{-7, 15}
Solve by Factoring: x2 + 8x - 65 = x - 5
x2 + 8x - 65 - x +5
x2 + 7x - 60 Find factors of -60 that sum 7
(x + 12)(x - 5)
x = {-12, 5}
Solve the following quadratic equation by factoring.
9x2 + 5x - 24= 8x2 + -5x
x2 + 10x - 24 Find factors of -12 that sum 10
(x + 12)(x - 2)
x = {-12, 2}
Solve the following quadratic equation by factoring:
-2m2 - 60m +72 = -8m2 - 3m
6m2 - 57m + 72 = 0
3(2m2 -19x + 24)
3(m2 - 19x + 48)Find product of 48 that sums -19
3(m - 3/2)(m - 16/2) = 3(2m -3)(m - 8)
{3/2, 8}
Solve the following quadratic equation by completing the square:
x2 - 8x + 13 = 0
4 +-sqrt 3
x2 - 8x + 13 = 0
(-8/2)2 = (x - 4)2 + 13 - 16 = (x - 4)2 - 3 = (x - 4)2 = 3 x = 4 +/- sqrt 3
x = 4 +/- sqrt 3
Solve By Square Rooting:
5x2+1=126
+/- 5
Solve by Square Root Method:
4x2 - 30 = 22
4x2 = 52
4x2 = 52 4 4
x2= 13
x = +/- sqrt of 13