j(x)=(x-1)^2+3 How does the function differ from the one above. Transformation: (the one above is y=x^2)

Question

help me with this

Answer 1

Hi Gina,

f(x) = x² is usually called a "parent" function, that is a parabola with a vertex at (0, 0)

f(x) = a(x - h)² + k has adjustments, a, h, and k that will change the shape and position of the "parent" parabola.

if a is more than 1, the parabola will be 'stretched' vertically. If a is less than 1, the parabola is 'shrunk' vertically.

If h and k are not zero, they will shift the vertex of the parabola to (h, k)

Your function j(x) = (x - 1)² + 3 has the same shape as y = x² but its vertex is not at (0, 0). Your h = 1 and k = 3. So, what are the coordinates of the vertex?