Write the quadratic function in the form f(x)= a(x-h)^2 + k

Algebra
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Write the quadratic function in the form f(x)= a(x-h)^2 +k

Then give the vertex of its graph.

f(x)= 3x^2 +18x +30

Oct 8th, 2015

Thank you for the opportunity to help you with your question!

to convert into vertex form, we use the principle of completing the square.

f(x)-30=3x^2+18x : add both sides with (b/2)^2

y-30=3(x^2+ 6x)

y-30+ 3()=3(x^2+6x ), the spaces will be used to balance the equation.

take half the coefficient of x on the right side; (1/2)*(6)=3. now square the results 3^2=9

Add 9 on both spaces in the previous equation.

y-30+3(9)=3(x^2+6x+9)

y-30+27=3(x+3)^2

y=3(x+3)^2 + 3

but (h,k) is the vertex h= -3 and k= 3

vertex is (-3, 3)

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 8th, 2015

I also need the quadratic function in the form : f(x)=

Oct 9th, 2015

sorry. i used y to make the calculations understandable. 

f(x)=3(x+3)^2+3

Oct 9th, 2015

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