1) Equation Forms
Vertex Form: y=a(x-h)^2+k
Factored Form: y=a(x-r)(x-s)
Standard Form: y=ax^2+bx+c
2) Ways of achieving Roots/X-Intercepts
Factored Form --> X Intercepts are R and S
Vertex Form --> Vertexes are H and K
Standard Form --> X Intercept : Factor through Decomposition or Quadratic Formula
Standard Form --> Vertex: Completing the square or Quadratic Formula to find X int, Average the X int, then substitute back in to find Y
3) Formulas
Quadratic Formula : used for find X intercepts from Standard Form Equation
4) Common word problems
-Speed/Velocity/Height problems relating to Rockets, or Balls. Assuming equation is given.
-Determine when the rocket will hit the ground.
-Find X intercept of the equation. Use the second Intercept where it visually hit's the X Axis representing the ground on the parabola.
-Determine the maximum height of the Rocket and at what time will it achieve that height
-Find the X intercept through quadratic formula if the equation cannot go through completing square to be converted to vertex form. Mean average the X Intercepts and replace the X into the equation to find Y. Y is your maximum height and X is the time at which the rocket achieves the maximum height.
-Determine the amount of time the rocket is above Z number of meters. (Z can be any value the question provides)
-Replace H, in your quadratic equation with Z and solve accordingly for the X intercept. The X intercepts will be your start/stop time. Your answer should be written like the following: (Start time) > (time reaching max height) > (end time).
-Revenue Questions
- Revenue = (Current price +/- Price decreased/increased X) (Current sales parameters +/- Number parameters decreased)
For example, If Bill Gates sells 15 copies a day of Windows 7 at the current price of $299, he would sell 4 more copies of Windows 7 per day if the price decreases $5.
X will be the amount of times increased in the price.
Equation would be: Revenue = (299-5X)(15 + 4X)
The amount you increase will be X.
Email onstudynotes@gmail.com if we missed any word problem scenarios. which we did.
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