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

Jun 13, 2016

The maximum value is at (1, -3)

#### Explanation:

This is the equation of a parabola.

The standard form is $y = a {x}^{2} + b x + c$

The axis of symmetry can be found from the formula

$x = \frac{- b}{2 a} , \text{ using the values from the given equation}$

$x = \frac{- 4}{2 \left(- 2\right)} = \frac{- 4}{- 4} = 1.$

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:

$y = - 2 {x}^{2} + 4 x - 5$

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

The maximum value is at (1, -3)