Solve by Factoring
Completing the Square and the Square Root Property
Quadratic formula
Imaginary Numbers and Complex Solutions
Graphing Quadratics
100
What's the first step to solve quadratics by factoring
Step 1. Write the equation in standard form.
100
What's the first thing you have to do to complete the square?
Divide by a, then move the constant.
100
When solving using the quadratic formula, what is the first 2 things you should do?
1st - make sure it is in standard form
(ax2 + bx + c = 0
2nd - Write down the values of;
a =
b =
c =
100
What is i = ?
sqrt(-1)
100
How is standard form written for a quadratic equation?
y = ax2 + bx + c
or
ax2 + bx + c = 0
200
Factor and solve the following:
12x^2 +3x= 0
x = 0 and x = -1/4
200
Solve 0 = x2 − 6x by completing the square.
x2 − 6x = 0
x2 − 6x + 9 = 0 + 9
(x -3)2 = 9
sqrt(x -3)^2 = sqrt9
x-3 = +- 3
x = 0
x = 6
200
DOUBLE
How many solutions will the following have?
2m2 + 2m − 12 = 0
b^2-4ac
Two rational solutions
200
What is
i^2
-1
200
How do you tell if a quadratic has a minimum or maximum?
The a-value
a-positive min
a-negative max
300
Solve this quadratics by factoring.
x2 + 2x = 3
x2 + 2x - 3 = 0
(x-1)(x+3) = 0
x = 1 or x = -3
300
Solve 0 = x2 − 25 by using the square root property.
x2 − 25 = 0
x2 = 25
(x)2 = 25
sqrt(x)^2 = sqrt25
x= +- 25
x = 5
x = -5
300
DOUBLE
Solve x2 + 4x - 21 = 0 by using quadratic formula.
a = 1, b = 4, and c = -21
x = 3 or -7
300
DOUBLE
Simplify the following:
sqrt(-20) * sqrt(-84)
-4sqrt(105)
300
What is the formula for x-coordinate of the vertex when the quadratic equation is in standard form?
x =- b/(2a)
400
DOUBLE
Solve this quadratics by factoring.
25x^2 +40x +16 = 0
x = -4/5
400
What are the roots for the following quadratic?
x^2+36 = 0
x=+-6i
400
Solve x2 - 8x + 14 = 0 using the quadratic formula.
a = 1, b = -8, and c = 14
x = -(-8) ±√ (-8)2 - 4(1)(14) / 2(1)
= 8 ±√ 8 / 2
= 5.41 and 2.59
400
Simplify the following:
(2 + 3i)(-4-5i)
7-22i
400
Graph the following:
y = x^2+2x+1
(-h, k)
500
Solve by factoring.
-12x^2+5x=-2
x = -1/4 or 2/3
500
Solve x2 - 6x + 7 = 23
x = -2,8
500
Solve 2x2 = 7x + 6 by using quadratic formula.
a = 2, b = -7, and c = -6
x = -(-7) ±√(-7)2 -4(2)(-6) / 2(2)
x = (7 ±√ 97) / 4
x =4.21 and -.71
500
Solve the following and write your answer as a complex number(use the quadratic formula):
5x^2+3x+3= 0
x = (-3+-isqrt51)/10
500
Graph the following:
y = -2x^2+3x+3
