Question

What is the axis of symmetry and vertex for the graph `y = -2x^2 - 6x + 1`?

Answer 1

Axis of symmetry`" "->x= -3/2`

Vertex`" "->(x,y)->(-3/2,11/2)`

Explanation:

Write as `y=-2(x^2+3x)+1`

Consider the 3 from `+3x`
`color(green)("Axis of symmetry "-> x_("vertex")=(-1/2)xx(3)=-3/2)`
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Substitute `x=-3/2` in the original equation to determine `y_("vertex")`

`color(brown)(y=-2x^2-6x+1)`

`color(blue)(=>" "y_("vertex")=-2(-3/2)^2-6(-3/2)+1)`

`color(blue)(=>" "y_("vertex")=-2(+9/4)-6(-3/2)+1)`

`color(green)(y_("vertex")=11/2)`

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