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

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

Step-by-step 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.

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x