MATH 3

Resources

Forms of Quadratic Equations

Standard- ax²+bx+c

c:y-intercept

Vertex- a(x-h)²+k

(h,k):vertex, x=h:axis of symmetry

Factored- a(x-r₁)(x-r₂)

r₁ and r₂: x-intercepts, roots, zeros

Ways to Solve a Quadratic Equation

Square Root method- use when there is no x term

Factoring- works sometimes

Graphing- always works if using DESMOS

Completing the Square- always works

Quadratic Formula-always works

Square Root Method

NO x term

Factoring

Must be set equal to zero

Factor out GCF

Factor quadratic

Set terms equal to zero

Constant can’t equal 0

Solve one step equations

Completing the Square

Solve using completing the square x²+8x+8=-7

X terms and constants on opposite sides of = x²+8x=-15

Half coefficient of x term, add to both sides x²+8x+16=-15+16

Factor left side to binomial squared, simplify right (x+4)²=1

Use square root to solve x+4=1 or x+4= -1

Solve one step equations x=-3 or x=-5

Quadratic Formula

Solve using quadratic formula 2x²+5x+6=-12

Make sure equation is set equal to 0 2x²+5x+18=0

Identify a, b,c and put in formula a=2, b=5, c=18

Put values in formula

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Simplify

The Number “i”

Remember the square root of a number is the number that is multiplied by itself to get that number. When you multiply a positive number by a positive number, the answer is positive. When you multiply a negative times a negative, the answer is positive. What is the square root of a negative number? It is not real. That is what i is for.

Trigonometric Functions

SohCahToa- What does it mean, stand for?

Soh- Sine= Opposite Cah- Cosine= Adjacent Toa- Tangent=Opposite

Hypotenuse Hypotenuse Adjacent

Hypotenuse

A

opposite

adjacent