SOLUTION: Here is the problem: Determine without graphing, whether the given quadratic function has a minimum value or maximum value. Then find the x and y coordinates of the minimum or the

Question 88807: Here is the problem:
Determine without graphing, whether the given quadratic function has a minimum value or maximum value. Then find the x and y coordinates of the minimum or the max point f(x)=X^2-2x-8
Here is what I have done
x=- b/2a
x=- -2/2(1)
x=2/2(1)
x=2/x
x=1
f(1)=(1)^2-2(1)-8
f(1)=(1)-2(1)-8
f(1)=(1)-2-8
f(1)=-1-9
f(1)=-9
Is this right?

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Given:
.
f(x)=X^2-2x-8
Here is what I have done
x=- b/2a <=== ok
x=- -2/2(1) <=== ok
x=2/2(1) <=== ok
x=2/x <=== should be 2/2
x=1 <=== ok
f(1)=(1)^2-2(1)-8 <=== ok
f(1)=(1)-2(1)-8 <=== ok
f(1)=(1)-2-8 <=== ok
f(1)=-1-9 <=== you probably meant -1 - 8
f(1)=-9 <=== ok
.
You used a good process. And the point you found (1,-9) is the correct point. But you didn't
mention whether is was a maximum or a minimum point. It is a minimum point and you can tell
that because the x^2 term is preceded by a + sign. If the x^2 term had been -x^2 then the
point you found would have been a maximum point on the curve.
.
You have the correct idea on how to do the problem.
.
Another thing you can tell about this graph from the work you have done is that the graph
crosses the x-axis at two points. You can tell this because the minimum point occurs where
y = -9. The graph is a parabola that rises from that point. Therefore, in rising the
parabola must cross the x-axis in two locations ... one to the left of x = +1 and one to
the right of x = +1 on the x-axis. Hope this makes sense. Anyhow, good work!!!
.

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