Question

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

Answer 1

The maximum value is at (1, -3)

Explanation:

This is the equation of a parabola.

The standard form is `y = ax^2 + bx + c`

The axis of symmetry can be found from the formula

`x = (-b)/(2a), " using the values from the given equation"`

`x = (-4)/(2( -2)) = (-4)/(-4) = 1.`

That means that as the Turning point will also lie on the axis of symmetry, we know the x-value of the turning point.

This parabola has a maximum T.P. because the value of "a" is negative.

To find the y-value, substitute `x = 1` into the equation:

`y = -2x^2 + 4x - 5`

`y = -2 +4 -5 = -3`

The maximum value is at (1, -3)