Answer :
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.
The vertex form of the given parabolic equation is [tex]y=2(x+3.5)^2+0.5[/tex] and it can be determine by simplifying and then rewriting the given equation in vertex form of parabola.
Given :
Equation - [tex]y = (x+3)^2+(x+4)^2[/tex]
The given equation represents a parabola and the vertex form of parabola is given by:
[tex]y=a(x-h)^2+k[/tex] --- (1)
Now, simplify the given equation as:
[tex]y = x^2+9+6x+x^2+16+8x[/tex]
[tex]y = 2x^2+14x+25[/tex] ---- (2)
Now, rewrite the equation (2) in form of equation (1).
[tex]y = 2(x^2+7x+12.5)[/tex]
[tex]y = 2((x+3.5)^2-12.25+12.5)[/tex]
[tex]y=2(x+3.5)^2+0.5[/tex]
Therefore, the vertex form of the given parabolic equation is [tex]y=2(x+3.5)^2+0.5[/tex]
For more information, refer the link given below:
https://brainly.com/question/11581519