How do you describe the end behavior for $f (x) = - x^{2} - 8 x - 15$ $f(x)=-x^2-8x-15$ ?

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Answer 1 · 2018-01-13T15:18:44

See below.

For end behaviour of a polynomial, we only have to look at the leading coefficient and degree. In this case:

$- x^{2}$ $-x^2$

as $x \to - \infty$ $x->-oo$ , $888 - x^{2} \to - \infty$ $color(white)(888)-x^2->-oo$

as $x \to \infty$ $x->oo$ , $888 - x^{2} \to - \infty$ $color(white)(888)-x^2->-oo$

$x^{2} > 0888$ $x^2>0color(white)(888)$ for all $RRcolor(white)(888)$ , so $color(white)(8)-x^2<0$ for all $RR$

Since the coefficient of $x^2<0$ , the parabola is of the form:

$nnn$

GRAPH:

graph{y=-x^2-8x-15 [-10, 5, -5, 4]}

How do you describe the end behavior for f(x)=-x^2-8x-15f(x)=−x2−8x−15f(x)=-x^2-8x-15?