How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=-2x^2+6?

Mar 26, 2016

Axis of symmetry at $x = 0$

Maximum $\to \left(x , y\right) \to \left(0 , 6\right)$

Explanation:

Given:$\text{ } y = - 2 {x}^{2} + 6$

The coefficient of ${x}^{2}$ is negative so the generic shape of the graph is $\cap$. Thus we have a maximum.

The maximum will occur at the axis of symmetry which is also ${x}_{\text{vertex}}$

As there is no $b x$ term from $y = a {x}^{2} + b x + c$ then the axis of symmetry is at $x = 0$

Otherwise it would be at $x = \left(\frac{b}{a}\right) \times \left(- \frac{1}{2}\right)$ In fact it is as

$x = \left(\frac{0}{- 2}\right) \times \left(- \frac{1}{2}\right) = 0$

color(blue)(y_("vertex")=-2(0)+6 = 6

color(blue)("So maximum "->(x,y)->(0,6)