Integrated Math I Formulas

Rate of Change

y1-y2 ------- x1-x2

Arithmetic Explicit Formula

An = A1 + D(N-1)

Exponential Function

f(x)= a X b^x

Slope Intercept to Standard Form

-Add or subtract to move the x and y to the same side X AND Y SHOULD BE ON THE SAME SIDE AT THE END

Arithmetic Recursive Formula

An =A n-1 + D

X-Intercept

F(x)= 3x + 4 Replace Y value with 0, or f(x) 0= 3x + 4 0= 3x - 4 -4=3x --------- = 1.33=x 3 3

Y-intercept

F(x)= 3x +4 Replace X value with 0 f(x)= 0x =4 f(x)= 4

Geometric Recursive Formula

Gn= G n-1 X R

Geometric Explicit Formula

Gn=G1 ^ n-1

Graphing Horizontal Lines

HOY formula The line is *H*orizontal Horizontal lines have zer*O* slope The line will cross the *Y* axis

Solving Linear Equations

The same as solving an equation *EXCEPT* If you multiply or divide both sides by a negative number, the INEQUALITY CHANGES DIRECTION

Linear Absolute Value

f(x)= a|x+b| + c

Quadratic Function

f(x)=ax^2+bx+c

Converting Arithmetic Sequences to Function forms

*Step 1:* Distribute *Step 2:* Combine Like Terms

Converting Standard to Slope Intercept Form

- subtract the x term in order to get the y term by itself -divide by the coefficient of y (coefficient is *5*y

Compound Interest

A = P(1+r)

Independent Value in Slope-Intercept Form

Plug in the dependent value and solve for x f(x)= -3 and f(x)=-2x - 1 -3= -2x - 1 +1 + 1 ________________ -2 = -2x x = 1

Linear Function

f(x)=mx+b

Graphing Vertical Lines

VUX formula The line is *V*ertical Vertical lines have *U*ndefined slope The lines will cross the *X* axis

Slope-Intercept Form

y=mx+b

Simple Interest

A = P + (R X P) X T

Solving Absolute Value Inequalites

*Step 1:* Isolate the Absolute value *Step 2:* Set up two inequalities. When you set up the second one, flip the sign. *Step 3:* Solve for the variable in both equations *Step 4:* Check your answer with the original problem ***TIP*** When you have a variable that is greater than a number, when you plug in a number for the variable, make it greater than the number EXAMPLE x > 3 5 > 3

Solving Absolute Value Equations

*Step 1:* Isolate the Absolute value ( get it alone) *Step 2:* Set up 2 equations. Since absolute value is the distance from 0, your equations will be negative and positive, left or right *Step 3:* Solve for the variable for both equations *Step 4:* Check your answers. Plug in the number you found for the variable as the variable. Often, only one or neither of them will work. Check with the original problem.

Converting Geometric Sequences to Function Forms

*Step 1:* Turn it into a fraction *Step 2:* Make the second number the denominator *Step 3:* Put the first number as the numerator *Step 4:* Take the second number and raise it to "n" ( separate to the denominator. The Second number is still a thing) *Step 5:* If the two don't have the same base, set them up to be multiplied. If they do have the same base, use properties of exponents to combine them. EXAMPLE Gn = 2 X 4^n-1 Fn = 2/4 X 4^n

Dependent Value in Slope-Intercept Form

y=3x-2 given value is 2 y=3(2) -2 y=4