Influence of coefficients a, b, c on the location of the parabola

The coefficient

a

$a$ sets branch direction and how "steep" the parabola is. •

a>0

— branches up;

a<0

— down. • The larger

|a|

, the narrower the parabola (

|y|

grows faster in magnitude for the same shift). • Multiplying the function by a number

k

scales all

y

-values:

y=k(ax^2+\ldots)

; if

k

is negative you also reflect across the

x

-axis.

a=0

is no longer quadratic — you get a line

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