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 + 2 a. minimum;

Click here to see ALL problems on Functions

Question 1061026: 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 + 2
a. minimum; - 1
b. maximum; 3
c. minimum; 3
d. maximum; - 1

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source):
You can put this solution on YOUR website!
Coefficient on the degree-two term is negative one, , so the graph for the parabola is concave downward and has vertex as a MAXIMUM.

You could convert f into standard form and read the point for the vertex.

------this step is Completing The Square.

Vertex is (-1,3).

Answer by MathTherapy(10552) (Show Source):
You can put this solution on YOUR website!
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 + 2
a. minimum; - 1
b. maximum; 3
c. minimum; 3
d. maximum; - 1

Leading coefficient is < 0, so function has a
That maximum value occurs at:
Therefore, maximum value is at f(- 1), and:
We then get:
That's all.......nothing too COMPLEX!

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 + 2 a. minimum; - 1