MPM2D Grade 10 Math Quadratics Relations Test

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.