SOLUTION: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = x^2 - 2x - 5 a. maximum; 1 b.

Algebra ->  Graphs -> SOLUTION: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value. f(x) = x^2 - 2x - 5 a. maximum; 1 b.      Log On


   

Question 1042942: Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then find that value.
f(x) = x^2 - 2x - 5
a. maximum; 1
b. minimum; 1
c. maximum; - 6
d. minimum; - 6
Answer by ikleyn(52772) About Me  (Show Source):
You can put this solution on YOUR website!
.
1. It has the minimum.
   Since it is a parabola opened up.

   It is the parabola opened up, because its leading coefficient is positive.


2.  The minimum is at x = 1.   (Option b)

    Because for the general quadratic function y = ax^2 + bx + c the min/max is at x = -b%2F2a.  

    It is -%28-2%29%2F%282%2A1%29 = 1 in your case.


3.  To get the value of the minimum, substitute this x=1 into the formula for your quadratic function. You will get

    f(x) = 1%5E2+-+2%2A1+-+5 = 1 - 2 - 5 = -6.

See the lesson Who is who in quadratic equations in this site.