Factoring
Factor the following:
3x^2+12x
GCF = 3x
3x(x+4)
Solve for x by taking the square root:
x^2=121
x=+-12
Solve by factoring and ZPP:
x^2+12x+36=0
6 * 6 = 36
6 + 6 = 12
(x+6)(x+6)=0
x=-6 and x=-6
Solve using the Quadratic Formula:
2x^2+7x+6=0
x=(-7+-sqrt(7^2-4(2)(6)))/(2(2))
x=0.5 and x=-3
How many real solutions does the following equation have:
x^2=-100
Can't square root a negative
No solutions
Solve:
(x+4)(x+8)=0
ZPP:
x+4=0 and x+8=0
x=-4 and x=-8
Factor the following:
x^2+8x-48
12 * -4 = 48
12 + -4 = 8
(x+12)(x-4)
Solve by taking the square root: (isolate the squared term first)
x^2+13=29
x^2=16
x=+-4
Solve by factoring and ZPP:
x^2-5x=0
GCF: x
x(x-5)=0
x=0 and x-5=0
x=0 and x=5
DAILY DOUBLE!
Solve using the Quadratic Formula:
3x^2-12x-15=0
x=(-(-12)+-sqrt((-12)^2-4(3)(-15)))/(2(3))
x=5 and x=-1
How many real solutions does the following equation have:
(x-3)(x+3)=0
Two real solutions
x=3 and x=-3
How many real solutions does the following equation have:
3x+4=13
One solution
x=3
Factor the following:
x^2-576
Difference of Perfect Squares
(x)2-(24)2
(x+24)(x-24)
Solve the following by taking the square root:
(x+3)^2=49
x+3=+-7
x+3=7 and x+3=-7
x=4 and x=-10
Solve by factoring and ZPP:
x^2-5x-24=0
x^2-5x-24=0
-8 * 3 = -24
-8 + 3 = -5
(x-8)(x+3)=0
x-8=0 and x+3=0
x=8 and x=-3
Solve using the Quadratic Formula:
x^2-10x-24=0
x=(-(-10)+-sqrt((-10)^2-4(1)(-24)))/(2(1))
x=-2 and x=12
A rocket is launched from a platform above the ground. It’s path is modeled by the function
h(x)=−4.9x^2+27x+12
, where x is the time in seconds and h(x) is the height of the rocket in
feet.
When does the rocket hit the ground?
Find the zeros using any method
Unfactorable --> Quadratic Formula
Positive answer makes sense so it hits the ground after 5.92 seconds
x=(-(27)+-sqrt((27)^2-4(-4.9)(12)))/(2(-4.9))
x=5.92 and x=-0.41
DAILY DOUBLE!
Solve:
(x-12)(3x+9)=0
ZPP:
x-12=0 and 3x+9=0
x=12 and 3x=-9
x=12 and x=-3