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

Asked by wiki @ in Mathematics viewed by 405 People

Answered by wiki @

we have

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

y=(x+3)^{2}+(x+4)^{2} \\y= x^{2} +6x+9+x^{2}+8x+16 \\y=2x^{2}+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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