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

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

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