What decides vertical shift in this Equation?

y=x²+4

y=x²+4

The term following x² is the factor on vertical shift. The +4 shifts 4 units up while -4 would shift down 4 units.

What part of the equation decides horizontal shift?

y=(x-h)²

y=(x-h)²

y=f(x+h) Shift the graph to the left h units.

y=f(x-h) Shift the graph to the right h units.

What will this equation look like on a graph?

y=(x+3)²-5

y=(x+3)²-5

The (x+3)² will shift the vertex 3 units to the left.

The -5 portion of the equation will shift the vertex down 5 units.

This equation's vertex will be (-3, -5) and will be in the lower left quadrant.

What part of this equation determines vertical stretch or compression?

y=1/2x

y=1/2x

If this number is <1 it will compress the parabola and widen the complex.

If this number is >1 it will stretch the parabola and narrow the complex.

_{What determines the reflection of an equation on the x-axis?}

y=-f(x)

y=-f(x) 

This is the reflection of the equation y=f(x) on the x-axis.

What determines the reflection of an equation on the y-axis?

y=f(-x)

y=f(-x)

This is a reflection of the equation y=f(x) on the y axis.

Circumference of a Circle

C=(pi)2r

or

C=(pi)d

Law of Exponents

a^maⁿ=

Law of Exponents

(a^m)ⁿ=

Law of Exponents

(ab)^m=

Law of Exponents

a^m/aⁿ=

Law of Exponents

(a/b)^m=

Perfect Cube Formula

a³-b³=(a-b)(a²+ab+b²)

Sum of Perfect Cube Formula

a³ + b³ = (a + b)(a² – ab + b²)

Difference of Perfect Cubes Formula

a³ – b³ = (a – b)(a² + ab + b²)

 SOAP

"Same sign"

"Opposite sign"

"Always"

"Positive"

a³ ± b³ = (a [same sign] b)(a² [opposite sign] ab [always positive] b²)

How can you rewrite this equation?

x^1/2

Area of a Circle

A=(pi)r²

-b+-sqrt b²-4ac

2a

y=a(x – h)²+ k, where (h, k) is the vertex

If the a<0 then the parabola will open downward.

If the a>0 then the parabola will open upwards.

Axis of Symmetry

x=-b/2a

Vertex

The vertex will be (h,k).

Vertex

(x,y)=(-b/2a,f(-b/2a))

y-intercept

You will solve for f(0) in the function.

x-intercept

Make the f(x)=0. Then use the Quadratic formula to solve for the x-intercept.

Discriminant

b²-4ac

y₂-y₁

x₂-x₁

x₁ cannot = x₂

How do you solve this equation?

x=a^y

Rewrite the equation in these terms.

y=log_ax

How do you solve this equation?

y=log₄64

You rewrite the equation in these terms and solve.

4^y=64

4³=64

y=3

What will this equation look like rewritten?

y=lnx

What is going to be the answer to this log?

a^log_aM=?

What is going to be the answer to this log?

log_aa^r=?

How can this be rewritten?

4log_a3=?

How can this be rewritten?

ln4-ln73=?

log_aM=?

log_aM=log_bM/log_ba

log_aM=logM/loga

log_aM=lnM/lna

A=P(1+r/n)^nt

A=Annual amount

P=present amount

r=interest rate

n=compound frequency

t=time

A=Pe^rt

A=Annual Amount

P=Present amount

e=natural log

r=interest rate

t=time

A(t)=A_oe^kt

A=Decay half life time

A₀=

k=Constant

t=

u(t)=T+(u₀-T)e^kt

u(t)=current temp of item

T=temp of surrounding medium

u₀=starting temp of item

t=time

k=constant