Question

Rewritten in vertex form please!!! Asap!!!

Answer 1

Answer:

vertex form:  $y=2(x+\dfrac{7}{2})^2+\dfrac{1}{2}$

B correct

Step-by-step explanation:

$y=(x+3)^2+(x+4)^2$

$y=x^2+9+6x+x^2+16+8x$

$y=2x^2+14x+25$

$y=2(x^2+7x)+25$

$y=2(x^2+7x+\dfrac{49}{4}-\dfrac{49}{4})+25$

$y=2(x+\dfrac{7}{2})^2+\dfrac{1}{2}$

Answer 2

Answer:

B

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

y = (x + 3)² + (x + 4)² ← expand and simplify

  = x² + 6x + 9 + x² + 8x + 16

  = 2x² + 14x + 25

To obtain vertex form use the method of completing the square

The coefficient of the x² term must be 1

Factor out 2 from 2x² + 14x

y = 2(x² + 7x) + 25

add/ subtract ( half the coefficient of the x- term )² to x² + 7x

y = 2(x² + 2($\frac{7}{2}$) x + $\frac{49}{4}$ - $\frac{49}{4}$ ) + 25

y = 2(x + $\frac{7}{2}$ )² - $\frac{49}{2}$ + $\frac{50}{2}$

y = 2(x + $\frac{7}{2}$ )² + $\frac{1}{2}$