Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form?

The vertex form of the given parabolic equation is and it can be determine by simplifying and then rewriting the given equation in vertex form of parabola.

Given :

Equation -

The given equation represents a parabola and the vertex form of parabola is given by:

 --- (1)

Now, simplify the given equation as:

 ---- (2)

Now, rewrite the equation (2) in form of equation (1).

Therefore, the vertex form of the given parabolic equation is

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y=(x+3)^2+(x+4)^2

First expand to a quadratic

y=2x^2+14x+25

next divide by the leading coefficient (2), or rather factor out the leading coefficient:

y=2[x^2+7x+12.5]]

Complete squares on the expression inside brackets

y=2[(x+3.5)^2-12.25+12.5]

=2[(x+3.5)^2+0.25]

=2[(x+3.5)^2+0.25]

Distribute:

y=2(x+3.5)^2+0.5

The last line above is the vertex form of the same parabola.

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