What is the value of h when the function h(x)=x^2−8x+14 is converted to vertex form?

llm

Answered on Sat May 28 2022

We have,

h(x)=x²−8x+14

Vertex form :

h(x) = a(x – h)² + k

We add and subtract the square of half the coefficient of x

h(x) = x² −8x + (-8/2)² - (-8/2)² + 14

h(x) = x² - 8x + (-4)² - (-4)² + 14

h(x) = x² - 8x + (-4)² - 16 + 14

The first three terms forms a perfect square trinomial by (a - b)² = a² - 2ab + b²

h(x) = (x - 4)2 - 2

Now, comparing it with vertex form, we get

h = 4