SOLUTION: Determine a quadratic function for y = ax^2+bx+c if its graph passes through the point (2,19) and it has a horizontal tangent at (-1,-8). I would appreciate it if someone could

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Question 1110500: Determine a quadratic function for y = ax^2+bx+c if its graph passes through the point (2,19) and it has a horizontal tangent at (-1,-8).
I would appreciate it if someone could help me with this!
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
If the tangent is horizontal, then the only
place it can be is at the vertex because no
other point on a quadratic has a horizontal
slope ( slope = zero )
----------------------------------------

The horizontal tangent is at ( -1, -8 )
The formula for the x-value of the vertex is:

and
( -1, -8 )

(1)
----------------------
( 2, 19 )

(2)
Add equations (1) and (2)
(1)
(2)
--------------------------

and

and
(2)
(2)
(2)
(2)
------------------------------
The equation is:

------------------------------
check answer:
( 2, 19 )

OK
(-1,-8 )

OK
Here's the plot:

Feel free to get another opinion on this