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Quadratic Functions: Express Curve in its equation in the form of...

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donatchange | Student, Grade 11 | eNoter

Posted February 25, 2012 at 6:52 PM via web

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Quadratic Functions: Express Curve in its equation in the form of f(x)=a(x+p)^2+q

How To Express Curve in its equation in the form of f(x)=a(x+p)^2+q


The curve: http://i44.tinypic.com/9k4aah.jpg

I know that f(x)=ax^2 + bx + c = a(x+p)^2+q,the equation of its symmetry is x= -p = -(b/2a), but how to solve this question?

 

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nathanshields | High School Teacher | (Level 1) Associate Educator

Posted February 25, 2012 at 9:38 PM (Answer #1)

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(-p,q) is the vertex so we have

`f(x)=a(x-3)^2+10`

Since the y-intercept is 7, we use the point (0,7) to find a:

`f(0)=9a+10=7`

`a=-1/3`

So we have

`f(x)=-1/3(x-3)^2+10`

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