Quadratic relations

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Chapter 4,5,6: Quadratic Relations

Ved Patel Sheil

Quadratics Math Concept map

Ved Anmol Panchal - Turner Fenton SS (2572)

Reformation

Ved Esmeralda Guzman

The Overview of Curriculum and the Approaches and Methods in Language Teaching related to approach, procedure, and design

Ved Emily Heredia

Linear and Non-Linear

independent and dependent varialbes

Non-linear relations

points do no lie along a line (curved)

second differences are equal

Linear relations

a straight line

first differences are equal

base quadratic

Vertex Form

Quadratic relations

y=ax^2

y=a(x-h)^2 +k

Min/Max Value

if the parabola opens downward it has a max value

if the parabola opens upward it has a min value

y intercept

set x as 0

Zeros

the x intercepts, set y as 0

ex.

The axis of symmetry is the "k" value

Vertical line drawn through the vertex

ex. if the equation was y=-2(x-1)^2 the axis of symmetry would be 1

The vertex of a parabola are the "h" and "k" values

the point (x,y) where the parabola changes direction

(h,k)

K

H

A

if the value of "a" is negative the parabola opens downward

a=-1

if the value of "a" is positive the parabola opens upward

a=1

Tpes Of Transformations

reflection

A parabola is reflected when the value of "a" is less than 0

a<0

vertical stretch

A parabola is vertically stretched when the value of "a" is more than 1 but less than -1

1

vertical compression

A parabola is vertically compressed when the "a" value is more than -1 but less than 1

-1

vertical translation

Determined by the "k" value in the y=a(x-5)^2+k formula The value of "k" can shift the parabola vertically up or down

if k<0 then it is translated down

if k>0 then it is translated up

horizontal translation

Determined by the "h" value in the y=a(x-5)^2 +k formula The value of "h" can shift the parabola horizontally right or left

if h<0 then it is translated the the left

if h>0 then it is translated to the right