Linear Functions
Draw a picture of a linear function.
Straight Line
What is the equation to find slope?
(y1-y2)/(x1-x2)
Describe an exponential graph.
Curved, increases/decreases quickly at first then slowly at the end
Solve the following equation for x.
16 = x + 2
x=14
What is the standard form of the quadratic function?
y= ax^2+bx+c
What is the equation for linear functions? Label the slope and y-intercept.
y=mx+b
m= slope
b=y-intercept
m= -2
What is the equation for exponential functions?
y=a(b)^x
Solve the equation for x.
3x + 2 = 17
x=5
What does the c-value do to the graph of a quadratic function?
Moves graph up or down.
Write the equation for a table with the slope of -4 and starting point at 6.
y=-4x+6
What is the slope of the points (-1, 3) (2, 8)?
m= 5/3
Write an equation for the following scenario:
Brayden opened a savings account at the bank and put in $500. The account has an interest rate of 6% each year.
y=500(1.06)^x
Solve the equation for x
3x^2 = 27
x = +3, -3
Expand the following linear terms into standard form.
(x+3)(x-4)
x^2-x-12
Create an equation for the following scenario to answer the question. Sydney ordered special bags of dino nuggets off Amazon. Each bag was $5.75, and he paid $3.00 in shipping. How much was 6 bags of dino nuggets?
y=5.75x+3
6 bags costs 37.50
What is the rate of change for this table of values?
x | 0 | 1 | 2 | 3 | 4 |
y | 6 | 12 | 18 | 24 | 30 |
rate of change = 6
Jeremiah bought a truck for $15000. This truck depreciates at a rate of 4% each year.
y=15000(.96)^x
Solve the system of equations for x.
y=3x+2
y=2x-3
x=-5
Expand the following linear terms into standard form.
(x-8)^2
x^2-16x+64
Jeremy orders BBQ Sauce from a soul food company. The sauce costs $8 a bottle with a $5 shipping fee. How much sauce did Jeremy buy if the total cost was $53?
53=8x+5
$53 buys 6 bottles
Find the rate of change of the following table of values.
x | 0 | 2 | 4 | 6 | 8 |
y | 14 | 10 | 6 | 2 | -2 |
rate of change = -2
Write an equation to answer the following question:
Jeremiah bought his truck for $15000. His truck depreciates at a rate of 4% each year. How much would his truck be worth in 10 years? Round to the nearest dollar.
y=15000(.96)^x
In 10 years the truck is worth $9972.
Solve the equation for x.
4x^2 + 36x = 0
x = {0, -9}
Expand the following linear terms into standard form.
(x+2)(x+3) + x(x-1)
2x^2+4x+6