SOLUTION: The graph of the quadratic function y = -x2 + x + 2 is a parabola. What is the range of the function? What is its vertex? What is the equation of the axis of symmetry?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The graph of the quadratic function y = -x2 + x + 2 is a parabola. What is the range of the function? What is its vertex? What is the equation of the axis of symmetry?       Log On


   

Question 998657: The graph of the quadratic function y = -x2 + x + 2 is a parabola.
What is the range of the function?
What is its vertex?
What is the equation of the axis of symmetry?

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
y=-x%5E2%2Bx%2B2---------as given, lead term coefficient indicates concave downward, vertex a maximum.
y=-%28x%5E2-x-2%29
y=-%28x%2B1%29%28x-2%29
Roots will be -1 and +2. Symmetry axis in the exact middle.

%28-1%2B2%29%2F2
1%2F2
highlight%28x=1%2F2%29-----------Axis of Symmetry


Evaluate y at x=1%2F2.
y=-%281%2F2%2B1%29%281%2F2-2%29
y=-%283%2F2%29%28-3%2F2%29
highlight%28y=9%2F4%29-------Vertex is ( 1/2, 9/4 ).

RANGE
All real values so that y%3C=9%2F4, because remember, this graph has a vertex as a maximum.