Question

Explain why the graph of the equation g(x)=-(x+1)^2-3 would be a parabola opening downward

Answer 1

We know that the parabola opens downwards because it has a negative leading coefficient.

Why the parabola opens downwards?

For any polynomial, the leading coefficient is the coefficient in the term where is the large exponent of the polynomial.

The sign of that coefficient will determine the end behavior of the graph of the polynomial.

For the case of the parabola, a positive leading coefficient means that the parabola opens upwards, while a negative leading coefficient will mean that the parabola opens downwards.

Now, if you look at our parabola:

g(x) = -(x + 1)^2 - 3

You can see that there is a negative sign, thus when we expand the parenthesis, we will end up with a negative leading coefficient:

g(x) = -x^2 - 2x + 1 - 3 = -x^2 -2x - 2

So we know that the parabola opens downwards.

If you want to learn more about parabolas:

brainly.com/question/4061870

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