Algebra Notes

Linear: Flat rate, constant rate

Exponential: expanding, growing

Quadratic: average rate

Formulas

  • Compound interest: A=P(1+r/n)^nt 

    • Interest Rate = (Simple Interest × 100)/(Principal × Time)

  • Quadratic (standard): y=ax^2+bx+c

  • Quadratic (vertex): y=a(x-h)^2+k

  • Exponential: y=ab^x

  • Linear (slope-intercept form): y=mx+b

  • Linear (point-slope form): y-y₁=m(x-x₁)

  • Slope: m = (y2 - y1)/(x2 - x1)

How to find the line of best fit

  1. Eye test: which function does it look like

  2. R and r^2:

  3. Residual Plot: The closer the dots are to 0 the better

Exponential Equation Using Two Points

  1. Identify the coordinates of two points from the graph.

  2. Plug both sets of coordinates into the general form of an exponential equation, so that you have two separate equations.

  3. Divide one equation by the other to eliminate the variable and solve for 

  4. Plug the value into either equation and solve for 

  5. Check your solution in the other equation.

How to solve:

  • A = lw = 200

  • l = w - 10

(Nonsense because length is by definition greater than width, but, ok)

  • Substitute:

200 = (w - 10)w

200 = w^2 - 10w

w^2 - 10w - 200 = 0

I can visually factor this:

(w - 20)(w + 10) = 0

w = 20, or w = -10 (ignore this solution)

w = 20, l = 10