Question

What is the axis of symmetry and vertex for the graph `y=3x^2-9`?

Answer 1

Axis of symmetry `->x=0`

Vertex`->(x,y)->(-9,0)`

Explanation:

Consider the standard form of `y=ax^2+bx+c`

Given:`" "y=3x^2-9`

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`color(blue)("General shape of the graph")`

The three in front of `x^2` is positive so the graph is of general shape `uu`. Suppose it was -3. Then the general shape for that scenario would be `nn`

So the shape of `uu` means we have a minimum.

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`color(blue)("Axis of symmetry")`

There is no term for the equation part `bx` thus the graphs axis of symmetry is `x=0`

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`color(blue)("Vertex")`

Suppose you just had `color(brown)(y=3x^2)` then the minimum would be at `color(brown)(y=0)`

However, we have `color(brown)(y=3x^2)color(blue)( -9)` so the vertex lowers by 9.

`color(green)(y_("vertex")->color(brown)(y=0color(blue)(-9))=-9)`