Question

Graph the following function and identify any shifts, stretches, and symmetry and x and y intercepts:

y = f(x) = (x - 3)^2 + 2

Answer 1

Explanation:

The parent function here is y = x^2, whose graph is that of a parabola that opens up and has its vertex at the origin, (0, 0).

Translating this parent graph 3 units to the right and then up by 2 units will produce the desired graph of y = f(x) = (x - 3)^2 + 2.

There are no stretches or symmetry.

y-intercept: let x = 0 and find y: 9 + 2 = 11. y-intercept is (0, 11).

x-intercept: let y = 0 and find x: (x - 3)^2 + 2 = 0 => (x - 3)^2 = -2. This has no real roots. Thus, there are no x-intercepts.