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.
