How many times does the graph of `y=x^2-16` intersect the `x` - axis?

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It intersects the `x` axis two times.

The algebraic way to see it is to factor `f(x)=x^2-16=(x+4)(x-4),` and the graph intersects the `x` axis precisely when `f(x)=0,` and this happens when `x=4` and `x=-4.`

The geometric way is to note that the graph of `y=x^2-16` is the same as the...

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It intersects the `x` axis two times.

The algebraic way to see it is to factor `f(x)=x^2-16=(x+4)(x-4),` and the graph intersects the `x` axis precisely when `f(x)=0,` and this happens when `x=4` and `x=-4.`

The geometric way is to note that the graph of `y=x^2-16` is the same as the graph of `y=x^2,` except shifted downward by 16 units. The graph of `y=x^2` (shown below in red) is a parabola opening upward and whose lowest point is `(0,0),` so the graph of `y=x^2-16` (in black) must intersect the `x` axis twice.

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