Formulas
What is slope-intercept form?
y=mx+b
f(x)=3x
Find f(2)
f(2)=3(2)=6
Given the following equations, solve for y:
y=3x
x=5
y=3(5)=15
Write an algebraic expression to represent the following verbal expression:
The sum of 2 and a number is the same as four times the same number minus 4
2+x=4x-4
What is the initial point for all functions on a graph called.
Hint: when the x-coordinate is zero.
The y-intercept
What is the standard form for linear functions?
ax+/-by=c
Find g(3)
g(3)=4(3)-5=12-5=7
Given the following equation, solve for x:
4(x+2)=2x-6
4x+8=2x-6
2x+8=-6
2x=-14
x=-7
Two containers are leaking at constant rates. Container A had 45 gallons and is leaking at a rate of 2 gallons per minutes. Container B had 60 gallons and is leaking at a rate of 3 gallons per minute. Let "x" represent time in minutes. How long, in minutes, will it take for the two containers to have the same amount of liquid, in gallons?
45-2x=60-3x
45+x=60
x=15 minutes
From the y-intercept, how to do find the next point for a linear function on a graph?
Hint: Think about how you calculate slope.
Rise/Run
What is the midpoint formula?
x-coordinate: (x1+x2)/2
y-coordinate: (y1+y2)/2
h(x)=4(x+2)
Find h(7)
h(7)=4(7+2)=4(9)=36
Given the following equations, solve for y.
x+2y=10
-x+4y=20
Use Elimination to eliminate the "x":
6y=30
y=5
Write the following verbal expression into an algebraic expression and solve for the variable.
Four times the sum of a number and 7 is equal to that same number times 7 minus 2.
4(x+7)=7x-2
4x+28=7x-2
28=3x-2
30=3x
x=10
Draw what an exponential growth looks like on a graph.
The picture should include an exponential function whereas the x-values increase, the y-values drastically increase at one point.
What is the standard form for Exponential Functions?
f(x)=a(1+/-r)x
s(t)=t2+6t-2
Find s(2)
s(2)=(2)2+6(2)-2=4+12-2=16-2=14
In the following equation, y=1200(0.85)x
the exponent represents and increment of time (years). If 7 years go by, solve for y. Round to the nearest hundredth.
y=1200(.85)7=384.69
You bought a car for $25,000. The car's value depreciates at a rate of 6% a year. How much will the car be worth in 8 years? Round your answer to the nearest cent.
y=25000(1-0.06)8=$15,239.22
For a quadratic function, where are the zeroes on a graph?
Hint: They are also called roots.
The x-intercepts or where the quadratic crosses the x-axis
What is the Recursive Formula for Arithmetic Sequences?
an=d(n-1)+a1
a(y)=3y2-4y+8
Find a(-2)
a(-2)=3(-2)2-4(-2)+8=3(4)+8+8=12+16=28
In the following quadratic, solve for the roots.
x2+10x+16=0
(x+2)(x+8)=0
x+2=0 x=-2
x+8=0 x=-8
There are 3 consecutive positive integers. The square of the smallest integer plus the product of the smallest and 7 is equal to 60. What are all three integers?
x2+7x=60
x2+7x-60=0
(x+5)(x-12)=0
x=12, x+1=13, x+2=14
Describe what a vertex for a quadratic function is on a graph.
The vertex is either the maximum or minimum point. It's where the y-value changes direction.