sketch the graph of quadratic function. identify vertex and x-intercepts

Question

f(x)=(x-3)squared-1

Answer 1

You know the value easily at x=3, you know that it is symettric about x=3, and an easy point to do in your head is x=8 and x=5

do those in your head, with the symettry about x=3, and you have the sketch.

Answer 2

Find a formula for the quadratic function whose graph has a y-intercept of y = 13 and zeros at x = 1, 6.