SOLUTION: I have to make a graph of this parabola: F(x) = x^2 -2x -15 I need the details of how each of the principals points are calculated. Thank you.

Question 541311: I have to make a graph of this parabola:
F(x) = x^2 -2x -15
I need the details of how each of the principals points are calculated.
Thank you.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The easiest point are the intercepts
x-intercept: (x,0)
y-intercept: (0,y)
To find x-intercept(s) ( may be 1 or 2 or none ),
set ( f(x) is the same as y )

Complete the square by dividing the coefficient
of the x term by 2, square it, and add it to both sides

take the square root of both sides

And, taking the negative root of

So, the x-intercepts ( also called roots ) are at
(5,0) and (-3,0)
---------------
To find the y-intercept ( only 1 ), set

y-intercept = (0, -15)
--------------------
Now you have 3 important points, also since the
coefficient of the term is positive, the
parabola has a minimum, not a maximum.
The minimum is always exactly between the
x-intercepts, or at ( (5 - 3)/2, y ) = ( 1, y), and to find y,

So, the vertex which is a minimum is at (1, -16)
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