Answer :
y=(x+3)²+(x+4)²
y=x²+6x+9+x²+8x+16
y=2x²+14x+25
y=2(x²+7x+3.5²-3.5²)+25
y=2(x+3.5)²-2*3.5² +25
y=2(x+3.5)²+0.5
y=x²+6x+9+x²+8x+16
y=2x²+14x+25
y=2(x²+7x+3.5²-3.5²)+25
y=2(x+3.5)²-2*3.5² +25
y=2(x+3.5)²+0.5
we have
[tex]y=(x + 3)^{2}+(x + 4)^{2}\\y=(x^{2} +6x+9) +(x^{2}+8x+16)\\y=2x^{2}+14x+25[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]y-25=2x^{2}+14x[/tex]
Factor the leading coefficient
[tex]y-25=2(x^{2}+7x)[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]y-25+2*(3.5^{2})=2(x^{2}+7x+3.5^{2})[/tex]
[tex]y-0.5=2(x^{2}+7x+12.25)[/tex]
Rewrite as perfect squares
[tex]y-0.5=2(x+3.5)^{2}[/tex]
[tex]y=2(x+3.5)^{2}+0.5[/tex]
the vertex is the point [tex](-3.5,0.5)[/tex]
therefore
the answer is
the equation rewritten in vertex form is equal to
[tex]y=2(x+3.5)^{2}+0.5[/tex]