Need help with quadratic equations: graphing

Hey so I'm having problems with a question regarding quadratic equations.
So first off we were given a sum e.g. y=(x - 3)^2 - 4 then we would put it into our calculator's graphing function then graph it on paper by working out the minimum/maximum, x intercepts and y intercept. But I'm stuck on this question.

What will be the position of the maximum or minimum in the graph of y=(x - a^2) + b, using patterns noticed above (previous questions). When will this equation have x intercepts?

So I reckon the maximum/minimum is (a,b) but I'm stuck as to what the x intercepts would be.

THANKS

Hi,

Your equation, y = (x - a)² + b, is the same as y = x² - 2ax + a²+b where c = a²+b

Using the quadratic formula and filling in these values gives:
. . . . . . _______________
-(-2a) ± √(-2a)² - 4(1)(a²+b)
-------------------------------------- = x
. . . . . . . 2(1)
. . . . ___________
2a ± √4a² - 4a² -4b
---------------------------- = x
. . . . . 2

. . . . ___
2a ± √-4b
--------------- = x <==2 x intercepts
. . 2

Since a = 1, the graph opens up, so the vertex of (a,b) is a minimum.

The y intercept has a y value equal to "c".

y intercept (0, a²+b)

I hope that helps!! :-)