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16259737
QUADRATICS
Description
Mind Map on QUADRATICS, created by Carmelia Taheri on 05/12/2018.
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grade 9
Mind Map by
Carmelia Taheri
, updated more than 1 year ago
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Created by
Carmelia Taheri
over 5 years ago
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Resource summary
QUADRATICS
Formulas
Standard Form
y=ax^2+bx+c
Find y- intercept
"c"
Find zeros
Quadratic formula
Vertex Form
y=a(x-h)+k
Find vertex, and AOS
Optimal value
k
Translations/ Transformations
"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
"h"
h>0
Horizontally translated to the right by lhl
h<0
Horizontally translated to the left by lhl
"k"
k>0
Vertically translated up by lkl
k<0
Vertically translated down by lkl
Factored Form
y=a(x-s)(x-t)
Find zeros/roots/x-intercepts
set y 0
Determining the number of roots
"a" and "k" have the same signs
No roots
"a" and "k" have different signs
two roots
"a" is irrelevant and k is not zero
One root
Graphing
1. Start with y=x^2 and transform all points
base formula
2. Plot the vertex and use new step pattern for other points
New step pattern= original step pattern (1,3,5) times "a"
Completing squares
To convert an equation to a vertex form
y=ax^2 + bx +c
perfect squares
b
word problems
Ask for max/min, or the x value that give the max/min
Factoring
2 terms
3 terms
4 terms
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