Answer: Amanda is not correct
The vertex is at (1.25, -3.125)
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Reason:
The x intercepts are 0 and 2.5
This is where the graph crosses the x axis. If we plugged in either x = 0 or x = 2.5, then we'd get f(x) = 0.
Find the midpoint of those values mentioned. Add them up, and divide by 2 to get the midpoint to be (0+2.5)/2 = 1.25
This is the x coordinate of the vertex.
Then plug that into the function to find the corresponding y coordinate of the vertex.
f(x) = 2x^2 - 5x
f(1.25) = 2(1.25)^2 - 5(1.25)
f(1.25) = -3.125
The vertex is located at (1.25, -3.125)
Amanda's x coordinate is correct, but the y coordinate isn't. Though her y coordinate isn't too far off.
I think I can see why she went with y = -3 since the lowest part of the graph is around this area. However, the lowest part of the parabola dips a tiny bit below y = -3. This is why it's better to use the equation rather than solely rely on the graph alone.
