What is the standard form of f(x)=x(x+9)  

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

f(x) = x(x+9)

First you need to expand brackets by multiplying with x:

==> f(x) = x*x + x*9

              = x^2 + 9x

==> f(x) = x^2 + 9x

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

f(x) = x(x+9)

Or y = x(x+9) is a parabola of 2nd degree.

y = x^2+9x

y = (x+9/2)^2- (9/2)^2

y+81/4 = (x+4.5)^2

y+20.25 = (x+4.5)^2.

The standard form of this type of formula is:

4a(y - k) = (x-h)^2 with its vertex  (x,y) at (h , k) and focus a units above (h,k) Or  focus at (h , k+a).

So the give parabola has its vertex at (-4.5 , -20.25) and focus at (-4.5 , -20.25+1/4) = (-4.5 , -20.00)

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