Question

What is the value of h when the function is converted to vertex form?

Answer 1

H=7.

To convert to vertex form, we complete the square.  This means we move the constant, c, to the other side.

y=x²-14x+29
y-29 = x²-14x+29-29
y-29=x²-14x

To find the number that we then add to both sides, we look at the value of b (coefficient of x).  We take half of that number; -14/2 = -7.  Then we square it; (-7)²=49.  This means we add 49 to both sides:

y-29+49=x²-14x+49

Now we combine like terms on the left:
y+20=x²-14x+49

Write the right hand side as a square:
y+20 = (x-7)²

Now move the 20 on the left back to the right by subtracting it from both sides:
y+20-20=(x-7)²-20
y=(x-7)²-20

The value of h is 7.