# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y-4 = – 2(x – 1)^2?

Jan 27, 2016

The axis of symmetry is $x = 1$.
The vertex is $\left(1 , 4\right)$.

#### Explanation:

$y - 4 = - 2 {\left(x - 1\right)}^{2}$

Put the equation into vertex form, $y = a {\left(x - h\right)}^{2} + k$, by adding $4$ to both sides of the equation.

$y = - 2 {\left(x - 1\right)}^{2} + 4$, where $a = - 2 , h = 1 , k = 4$

The axis of symmetry is the vertical line that divides a parabola into two equal halves. For an equation in vertex form, the axis of symmetry is $x = h$.

The axis of symmetry is $x = 1$.

The vertex is the minimum or maximum point of a parabola. In this case, because $a = - 2$, the parabola opens downward and the vertex is the maximum point.

The vertex in vertex form is $\left(h , k\right)$.
The vertex is $\left(1 , 4\right)$.

graph{y=-2(x-1)^2+4 [-10, 10, -5, 5]}