Fantastic
Factoring
Factoring
Solve by factoring
x2 - 8x - 20 = 0
(x-10)(x+2)=0
x=10,-2
Find the number that completes the square.
x2 - 24x + ______
(-24/2)2
144
Find the value of the discriminant and determine the number of real solutions.
2x2+5x-4=0
discriminant = b2-4ac
d = (5)2-4(2)(-4)
d = 57
2 real solutions
What do you have to do first to solve quadratics equation by taking square roots?
Isolate the squared part
What is the zero product property?
If ab = 0, then a = 0, or b = 0
Solve by factoring.
3x2 - 12x=0
3x(x-4)=0
x = 0,4
Find the number that completes the square.
x2 + (1/2)x + ______
1/16
Find the value of the discriminant and determine the number of real solutions.
x2 + 6x + 11 = 0
d = (6)2-4(1)(11)
d = -8
No real solutions
Solve this equation by taking square roots.
2x2 + 1 = 73
2x2 = 72
x2 = 36
x= ±6
Find the approximate solutions rounded to the tenth.
x = 5±√2
x = 6.4, 3.6
Solve by factoring.
2x2 + 5x = 3
2x2+5x-3=0
(2x-1)(x+3)=0
x=1/2, -3
Solve by completing the square.
x2 - 6x - 16 = 0
x2-6x=16
x2-6x+9=16+9
(x-3)2=25
x-3=±5
x=3±5
x = 8,-2
Solve by quadratic formula.
x2 -4x+7=0
x = [4 ±√16-4(1)(7)] / 2(1)
x = [4 ±√16-28] / 2
x = [4 ±√-12] / 2
x = NO SOLUTION (negative under square root)
Solve this equation by taking square roots.
3x2 - 10 = 62
3x2 = 72
x2 =24
x = ±2√6
Write the quadratic formula from memory.
x = (-b± √b2-4ac)/2a
Solve by factoring.
x3 = 36x
x3-36x=0
x(x2-36)=0
x(x+6)(x-6)=0
x = 0, 6, -6
Solve by completing the square
x2- 4x - 1 =0
x2- 4x = 1
x2- 4x +4 =1+4
(x-2)2=5
x-2=±√5
x = 2 ± √5
Solve x2 - 8x + 14 = 0 using the quadratic formula.
x =[ 8 ± √64-4(1)(14) ] / 2(1)
x = [8 ± √8 ] / 2
x = [ 8 ± 2√2 ] / 2
x = 4 ± √2
Solve this equation by taking square roots.
(x-4)2 - 16 = 0
(x-4)2 = 16
x- 4 =± 4
x = 4 ± 4
x = 0 or 8
If the discriminant is a perfect square, the solutions will be _____________
rational
Solve by factoring.
(3x + 7)(x - 3) = -16
3x2-9x+7x-21=-16
3x2-2x-5=0
(3x-5)(x+1)=0
x = 5/3,-1
Solve by completing the square.
5r2 = 40r + 5
r2 - 8r = 1
r2 - 8r +16 = 1+16
(r-4)2=17
r-4=±√17
x = 4 ±√17
Solve 2x2 = 7x + 6 by using quadratic formula.
2x2 - 7x - 6 = 0
x = [ 7 ±√49 - 4(2)(-6) ] / 2(2)
x = (7 ±√ 97) / 4
Solve this equation by taking square roots.
2(3x+2)2 - 8 = 0
2(3x+2)2 =8
(3x+2)2 = 4
3x+2 = ± 2
3x = -2±2
x = (-2±2)/3
x = 0 , -4/3
The quadratic formula is derived from standard form using which method?
Completing the square