SOLUTION: For the given function, (a) determine whether the graph opens upward or downward, (b) find the axis of symmetry, (c) find the vertex, (d) find the y-intercept, and (e) graph the fu

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: For the given function, (a) determine whether the graph opens upward or downward, (b) find the axis of symmetry, (c) find the vertex, (d) find the y-intercept, and (e) graph the fu      Log On


   

Question 884242: For the given function, (a) determine whether the graph opens upward or downward, (b) find the axis of symmetry, (c) find the vertex, (d) find the y-intercept, and (e) graph the function.
Equation:
f(x) = -2x² + 8x + 5
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Complete the square to get into vertex form.
y=-2x%5E2%2B8x%2B5
y=-2%28x%5E2-4x%29%2B5
y=-2%28x%5E2-4x%2B4%29%2B5%2B2%284%29
y=-2%28x-2%29%5E2%2B13
Since the multiplier on the %28x-2%29%5E2 term is negative, it opens downwards.
The vertex is (2,13).
The axis of symmetry is x=2.
The y intercept is
y=-2%280-2%29%5E2%2B13
y=-8%2B13
y=5
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