Understanding Parabolas As Translations

(Your goal today is for you to prove the quadratic formula)

Understanding Parabolas as Translations

Parabola: f (x) = ax + bx + c

1. Use the information from lecture about vertical and horizontal trans-

lations to graph the following parabolas on the axes provided below.

Label the coordinates of vertex of each parabola on the graph.

(a) y = x

(b) y = (x

5) + 3

2. Explain (using translations and the examples above) why when a

quadratic equation is written in y = a(x

h) + k form, the ver-

tex of the parabola can be read as (h,k). We will call this form of a

quadratic function vertex form. (Don’t worry about what the letter

a is doing there yet)

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