Question

How do you find the axis of symmetry, and the maximum or minimum value of the function `2x^2-5x+4=0`?

Answer 1

Min `(5/4, 7/4)`

Explanation:

`y = 2x^2 - 5x + 4`
x-coordinate of vertex, or of the axis of symmetry:
`x = -b/(2a) = 5/4`
y-coordinate of vertex, with `x = 5/4`:
`y(5/4) = 2(25/16) - 5(5/4) + 4 = 25/8 - 25/4 + 4 = 7/4`.
Since a > 0, the parabola opens upward, there is min at vertex.
Min `(5/4, 7/4)`
graph{2x^2 - 5x + 4 [-5, 5, -2.5, 2.5]}