Square Root Property
Completing the Square
Quadratic Formula
Factoring
Misc.
100
Solve using the square root property.
x^2-36=0
x^2=36
x=6 or x=-6
100
What value should be added to each side of the equation to complete the square?
x^2+16x=13
64
100
What is the quadratic formula?
x=(-b+-sqrt(b^2-4ac))/(2a)
100
Solve by factoring.
x^2-4x-12=0
(x+2)(x-6)=0
x=-2, x=6
100
What part of the quadratic formula is the discriminant?
b^2-4ac
200
Solve using the square root property.
2x^2-50=0
2x^2=50
x^2=25
x=5 or x=-5
200
What value should be added to each side of the equation to complete the square?
9x^2-24x=-5
16
200
Calculate the discriminant. How many real solutions for this equation exist?
3x^2-4x-8=0
4^2-4(3)(-8)
16+96
112
Two Solutions
200
Solve by factoring.
2x^2-7x=4
2x^2-7x-4=0
(2x+1)(x-4)=0
2x+1=0, x-4=0
2x=-1, x=4
x=-1/2, x=4
200
Simplify the radical. Show your steps.
sqrt300
sqrt(2*2*3*5*5)
sqrt(4*25*3)
sqrt(4)*sqrt(25)*sqrt(3)
2*5*sqrt(3)
10sqrt(3)
300
Solve using the square root property.
1/2 x^2-3=5
1/2x^2=8
x^2=16
x=4 or x=-4
300
Elias is solving by completing the square. Write out the next line of his solution.
4x^2+28x=-10
4x^2+28x+49=-10+49
(2x+7)^2=39
300
Calculate the discriminant and determine how many real solutions exist.
2x^2-5x=-3
2x^2-5x+3=0
a= 2, b=-5, c=3
5^2-4(2)(3)
25-24
1
2 Solutions
300
Kiah is solving by factoring. Finish the problem for her.
16x^2-22x-3=0
(8x+1)(2x-3)=0
8x+1=0, 2x-3=0
8x=-1, 2x=3
x=-1/8, x=3/2
300
What is the vertex of the graph of the function?
f(x)=2x^2-8x+3
x=-b/(2a)
x=8/4=2
2(2)^2-8(2)+3=-5
(2,-5)
400
Solve using the square root property.
(x+5)^2+7=56
(x+5)^2=49
x+5=7 or x+5=-7
x=2 or x=-12
400
Sabrina is solving by completing the square. Finish the problem for her. Make sure that her final answer is in simplest radical form.
9x^2+18x=4
9x^2+18x+4=4+4
(3x+2)^2=8
3x+2=+-sqrt8
3x=-2+-sqrt8
x=(-2+-sqrt8)/3
x=(-2+-2sqrt2)/3
400
Solve using the quadratic formula.
8x^2+6x+1=0
a=8, b=6, c=1
36-4(8)(1)=36-32=4
x=(-6+-sqrt(4))/16
x=(-6+-2)/16
x=-1/2 or x=-1/4
400
Solve by factoring.
4x^2+4x-15=0
(2x+5)(2x-3)=0
2x+5=0, 2x-3=0
2x=-5, 2x=3
x=-5/2, x=3/2
400
Draw a parabola. Label it vertex, axis of symmetry, and zeros.
500
Solve using the square root property.
1/4(3x+2)^2=9
(3x+2)^2=36
3x+2=6 or 3x+2=-6
3x=4 or 3x=-8
x=4/3 or x=-8/3
500
Solve by completing the square.
x^2-10x+5=0
x^2-10x=-5
x^2-10x+25=-5+25
(x-5)^2=20
x-5=+-sqrt20
x=5+-sqrt20
x=5+-2sqrt5
500
Solve using the quadratic formula.
5x^2-7x=-3
5x^2-7x+3=0
a=5, b=-7, c=3
(-7)^2-4(5)(3)
49-60
-11
no real solution
500
Solve by factoring.
12x^2+x-20=0
(3x+4)(4x-5)=0
3x+4=0, 4x-5=0
3x=-4, 4x=5
x=-4/3, x=5/4
500
Which two methods for solving quadratic functions are basically the exact same thing?
Completing the Square & The Quadratic Formula