QUADRATICS

QUADRATICS

Formulas
1. Standard Form
  1. y=ax^2+bx+c
    1. Find y- intercept
      1. "c"
    2. Find zeros
      1. Quadratic formula
2. Vertex Form
  1. y=a(x-h)+k
    1. Find vertex, and AOS
      1. Optimal value
        k
    2. Translations/ Transformations
      1. "a"
        Stretches
        lal>1
        Vertically stretches by factor of lal
        compression
        0<lal<1
        Vertically compresses by factor of lal
        Reflection
        a<0
        Reflected in x-axis
      2. "h"
        h>0
        Horizontally translated to the right by lhl
        h<0
        Horizontally translated to the left by lhl
      3. "k"
        k>0
        Vertically translated up by lkl
        k<0
        Vertically translated down by lkl
3. Factored Form
  1. y=a(x-s)(x-t)
    1. Find zeros/roots/x-intercepts
      1. set y 0
Determining the number of roots
1. "a" and "k" have the same signs
  1. No roots
2. "a" and "k" have different signs
  1. two roots
3. "a" is irrelevant and k is not zero
  1. One root
Graphing
1. 1. Start with y=x^2 and transform all points
  1. base formula
2. 2. Plot the vertex and use new step pattern for other points
  1. New step pattern= original step pattern (1,3,5) times "a"
Completing squares
1. To convert an equation to a vertex form
2. y=ax^2 + bx +c
  1. perfect squares
    1. b
3. word problems
  1. Ask for max/min, or the x value that give the max/min
Factoring
1. 2 terms
2. 3 terms
3. 4 terms

Resource summary

	Created by Carmelia Taheri over 5 years ago