Question

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

Note: Vertex form is g(x)=a(x−h)2+k .

g(x)=x2−6x+14

Answer 1

Answer:  The value of 'h' is 3.

Step-by-step explanation:  Given that the vertex form of a function is given by

$g(x)=a(x-h)^2+k~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the value of 'h' when the following function is converted to the vertex form.

$g(x)=x^2-6x+14~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (ii), we have

$g(x)=x^2-6x+14\\\\\Rightarrow g(x)=x^2-2\times x\times 3+3^2-3^2+14\\\\\Rightarrow g(x)=(x-3)^2-9+14\\\\\Rightarrow G(x)=(x-3)^2+5.$

Comparing it with the vertex form (i), we get

$h=3.$

Thus, the value of 'h' is 3.

Answer 2

The value of h in the vertex form is -3.

How to find the value of h?

in the vertex form:

g(x)=a(x−h)^2 + k

h is the x-value of the vertex.

Remember that for the general quadratic equation:

y = a*x^2 + b*x + c

The vertex is at:

h = -b/2a

So in our equation:

g(x) = x^2 - 6x + 14

We will have:

h = -(-6)/2*1 = 3

h = 3

That is the value of h.

If you want to learn more about quadratic equations, you can read:

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