Examples of Math Problems: The graph is a parabola with vertex (3,-8) and passing through the origin. Write the quadratic equation of this graph.

Friday, September 6, 2013

The graph is a parabola with vertex (3,-8) and passing through the origin. Write the quadratic equation of this graph.

We use the Standard Form:
%0D%0Ay=a%2A%28x-h%29%5E2%2Bk%0D%0A

%0D%0Ay=a%2A%28x-h%29%5E2%2Bk%0D%0A

from the vertex we get:
%0D%0Ay=a%2A%28x-3%29%5E2-8%0D%0A

%0D%0Ay=a%2A%28x-3%29%5E2-8%0D%0A

since the origin is on the graph,
%0D%0A0=a%2A%280-3%29%5E2-8%0D%0A

%0D%0A0=a%2A%280-3%29%5E2-8%0D%0A

9a=8

a=9%2F8

so we can write
%0D%0Ay=%289%2F8%29%2A%28x-3%29%5E2-8%0D%0A

%0D%0Ay=%289%2F8%29%2A%28x-3%29%5E2-8%0D%0A

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