Completing the Square
Complete the square and rewrite as perfect square factors:
x2 + 6x + ____
What is
x2 + 6x + 9 = (x + 3)2
Solve: f2-14f+13=0
f= 13 or 1
x2 +10x + c
25
Factor
x2 - x - 12
What is
(x - 4)(x + 3)
The intercept form of
2x2 + 9x - 5 ?
(2x - 1)(x + 5)
Complete the square and rewrite as perfect square factors:
x2 + 16x + ____
What is
x2 + 16x + 64 = (x + 8)2
Solve:
(x+ 4)(2x - 1) = 0
x = {-4, 1/2}
x2 - 30x+ c
225
Factor
2x2 + 9x + 10
What is
(2x + 5)(x + 2)?
The standard form of
-2(x+3)2 - 10
What is
-2x2 - 12x - 28
Complete the square and rewrite as perfect square factors
x2 - 20x + ____
What is
x2 - 20x + 100 = (x - 10)2
Solve: 5x2 - 3x - 2 = 0
x= 1 or -2/5
x2 -24x + c
144
Factor
6x2 + 5x + 1
What is
(2x + 1)(3x +1)?
The three forms of
x2 + 8x - 9
What are
standard form: x2 + 8x - 9
intercept form: (x - 1)(x + 9)
vertex form: (x + 4)2 - 25
Complete the square and rewrite as perfect square factors
x2 - 9x + ____
What is
x2 - 9x + 81/4 = (x - 9/2)2
Solve:
2x2 + 2x - 7 = 0
x={(-2+-2sqrt15)/4}
or
{(-1+-sqrt15)/2}
x2 + 3x + c
9/4
Factor
4x2 - 13x - 12
What is
(4x + 3)(x - 4)?
The three forms of
x2 - 6x + 8
What are
standard form: x2 - 6x + 8
intercept form: (x - 2)(x - 4)
vertex form: (x - 3)2 - 1
Complete the square and rewrite as perfect square factors
x2 + 7x + ____
What is
x2 + 7x + 49/4 = (x + 7/2)2
Solve:
2x2 + 2x + 9 = 0
x={(-2+-2isqrt17)/4}
or
{(-1+-isqrt17)/2}
x2 - 11x + c
121/4
Factor
5x2 - 12x + 4
What is
(5x - 2)(x - 2)?
The three forms of
4x2 + 8x + 3
What are
standard form: 4x2 + 8x + 3
intercept form: (2x + 3)(2x +1)
vertex form: 4(x+1)2 -1