Question

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

Answer 1

option B

Explanation:

Given in the question an equation y = (x+3)² + (x+4)²

Step 1

Expand this equation

y = (x+3)² + (x+4)²

y = (x²+9+6x) + (x²+16+8x)

y = 2x² + 14x + 25

Step 2

Find the minimum point of the parabola equation, y = 2x² + 14x + 25

y = ax² + bx +c

x = -b/2a

= -14/2(2)

= -14/4

= -7/2

Step 3

Find the vertex point by plugging value of x in the equation

y = 2(-7/2)² + 14(-7/2) + 25

= 49/2 - 49 + 25

= 1/2

vertex (h,k)

vertex (-7/2 , 1/2)

Step 4

vertex form

y = a(x - h)²+ k

y = 2(x + 7/2)² + 1/2