Plotting a graph using parallel transfers

Why vertex form helps

The standard form

y=ax^2+bx+c

is sometimes harder to read than the vertex (canonical) form:

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

Here

(h;k)

are the coordinates of the vertex of the parabola. The number

a

is as before: "stretch", opening of the branches, and their direction. Substitution shows

h=x_v

and

k=y_v

. Completing the square turns the formula

x_v=-\frac{b}{2a}

from the previous lesson into parameters

h,k

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

y=ax^2

translated by the vector

(h,k)

from the origin

Axis of symmetry: the line

x=h

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