SOLUTION: The question states, "sketch a parabola with real roots and a turning point of (0,-7). Is the turning point a minimum or maximum value for f(x)?" thanks

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: The question states, "sketch a parabola with real roots and a turning point of (0,-7). Is the turning point a minimum or maximum value for f(x)?" thanks      Log On


   



Question 677707: The question states, "sketch a parabola with real roots and a turning point of (0,-7). Is the turning point a minimum or maximum value for f(x)?"
thanks

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It sounds like it could be either one.
The x-coordinate of the vertex is at
+-b%2F%282a%29+ where the equation looks like
+y+=+ax%5E2+%2B+b%2Ax+%2B+c+
The turning point is at (0,-7), so
+-b%2F%282a%29+=+0+
+b+=+0+
Now I have
+y+=+ax%5E2+%2B+c+
+-7+=+a%2A0%5E2+%2B+c+
+c+=+-7+
------------
It looks like +a+ can be any (+) or (-)
number since it just controls the shape
( narrow or wide ) and the direction
( open down or open up )
I'll say +a+=+3+
+y+=+3x%5E2+-7+ answer
Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+3x%5E2+-+7+%29+