Quadratic relations

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Grammar Translation Method

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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