Question

How do you use the important points to sketch the graph of `Y=x^2 - 16`?

Answer 1

y-intercept = Vertex`->(x,y)=(0,16)`
x-intercept at point: `(4,0)" and "(-4,0)`

Explanation:

Compare to `y=x^2` which is of shape `uu` and the vertex is at the point`(x,y)=(0,0)`

Now include the `-16` and it drops the whole thing down by 16.

So the vertex for `y=x^2-16` is at:

`color(blue)("Vertex"->(x,y)=(0,-16)`
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To determine the x-intercepts set `y=0` giving

`y=0=(x^2-4^2) larr`always be on the lookout for this one

`0=(x-4)(x+4)`

Set `x-4=0 -> x=+4`
Set `x+4=0->x=-4`