Question

Which equation is y = (x + 3)2 + (x + 4)2 rewritten in vertex form? mc010-1.jpg mc010-2.jpg y = 2(x + 7)2 – 73 y = (x + 7)2 – 24

Answer 1

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

Answer 2

we have

$y=(x + 3)^{2}+(x + 4)^{2}\\y=(x^{2} +6x+9) +(x^{2}+8x+16)\\y=2x^{2}+14x+25$

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

$y-25+2*(3.5^{2})=2(x^{2}+7x+3.5^{2})$

$y-0.5=2(x^{2}+7x+12.25)$

Rewrite as perfect squares

$y-0.5=2(x+3.5)^{2}$

$y=2(x+3.5)^{2}+0.5$

the vertex is the point $(-3.5,0.5)$

therefore

the answer is

the equation rewritten in vertex form is equal to

$y=2(x+3.5)^{2}+0.5$