Question

The following graph of f(x) = x^2 has been shifted into the form f(x) = (x − h)^2 + k:

It is a parabola with the vertex 4, 1
What is the value of k?
99 pts because ¯\_(ツ)_/¯

Answer 1

k = 1

Explanation:

f(x) = x^2 has vertex at (0,0)

new form f(x)=(x-h)^2+k w vertex @ (4,1)

at vertex, f(x) is at minimum: because (x-h)^2 > 0, the minimum = k

k = 1

Answer 2

h = 5 or h = 3

Explanation:

f(x)=(x-h)^2 is a parabola

The vertex of a parabola is its lowest or highest point.

So (4,1) is a point on f(x)

substituting into the new equation, 1 = (4-h)^2

4-h = 1 or 4-h = -1

h = 5 or h = 3