Determine the vertex of the curve y=x^2 + 8x + 12.

Question

Be able to help my kids with there algebra work and lern to help my kids 

 

Answer 1

The vertex of a parabola can be found by taking values from the standard form

 

Vextex = (h,k) = (-b/2a, c- b²/4a)

 

In this case

a = 1

b = 8

c = 12

 

 

h = -8/(2*1)

k = 12 - 8²/(4*1)

 

h = -4

k = -4

 

So the vertex is found at (-4,-4)

Answer 2

The vertex has coordinate (h, k).  To find h, we use the formula

 

h = -b / 2a

 

where:

a = 1

b = 8

c = 12

 

h = -8 / (2*1)

h = -4

 

Now, we find k by evaluating y when x=h.

 

k = y(h)

 

k = (-4)² + 8(-4) + 12

 

k = 16 - 32 + 12

 

k = 32 + 12

 

k = -4

 

 

The vertex is (-4, -4).