Question

The following graph of f(x) = x2 has been shifted into the form f(x) = (x − h)2 + k: a parabola with a vertex of 2, 3 What is the value of k?

Answer 1

We are given

$f(x)=x^2$

and it has been shifted to get form

$f(x)=(x-h)^2+k$

where

vertex is (h,k)

and we are given vertex as (2,3)

now, we can compare

$(h,k)=(2,3)$

and then we can solve for k

and we get

$k=3$..............Answer

Answer 2

The value of $k$ is $3$ in the equation of the parabola $f(x)=(x-h)^2+k$ with the vertex at $(h,k)$.

The given function of the curve is $f(x)=x^2$ which is being shifted to  $f(x)=(x-h)^2+k$ with the vertex at $(h,k)$.

According to the question, $(2,3)$ is the vertex of the parabola.

So, compare the parametrs,

$(h,k)\rightarrow (2,3)\\h=2\\k=3$

Hence, the value of $k$ is $3$ in the equation of the parabola $f(x)=(x-h)^2+k$ with the vertex at $(h,k)$.

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