Answer:
y=2(x+3.5)^2+0.50
Step-by-step explanation:
we have
y=(x+3)^2+(x+4)^2
y=x^2+6x+9+x^2+8x+16
y=2x+14x+25
rewrite now in vertex form
Group terms that contain the same variable, and move the constant to the opposite side of the equation
y-25=2x^2+14x
Factor the leading coefficient
y-25=2(x^2+7x)
Complete the square. Remember to balance the equation by adding the same constants to each side
y-25+24.50=2(x^2+7x+3.5^2)
y-0.50-2(x^2+7x+12.25)
Rewrite as perfect squares
y-0.50=2(x+3.5)^2
y=2(x+3.5)^2+0.50
the vertex is the point (-3.5,0.50)
therefore the answer is
y=2(x+3.5)^2+0.50
