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

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Answer 1 · 2016-03-26T20:59:04

Axis of symmetry at $x=0$

Maximum $->(x,y)->(0,6)$

Given: $" "y=-2x^2+6$

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

The maximum will occur at the axis of symmetry which is also $x_("vertex")$

As there is no $bx$ term from $y=ax^2+bx+c$ then the axis of symmetry is at $x=0$

Otherwise it would be at $x=(b/a)xx(-1/2)$ In fact it is as

$x=(0/(-2))xx(-1/2)=0$

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

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

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