for the quadratic function ( f(x)=-x^{2}-8x ), answer parts (a) through (f)\na. the ( y )-intercept is…

for the quadratic function ( f(x)=-x^{2}-8x ), answer parts (a) through (f)\na. the ( y )-intercept is 0\n(type an integer or a simplified fraction.)\nb. there is no ( y )-intercept.\nwhat is the ( x )-intercept? select the correct choice below and, if necessary, fill in the answer box \ncomplete your choice\na. the ( x )-intercept(s) is/are ( -8,0 )\n(type an integer or a simplified fraction. use a comma to separate answers as needed )\nb. there is/are no ( x )-intercept(s)\n(c) use parts (a) and (b) to graph the function.\nuse the graphing tool to graph the function.\n(d) find the domain and the range of the quadratic function.\nthe domain of ( f ) is ( (-infty,infty) ).\n(type your answer in interval notation.)\nthe range of ( f ) is ( (-infty,16 ).\n(type your answer in interval notation )\n(e) determine where the quadratic function is increasing and where it is decreasing.\nthe function is increasing on the interval ( (-infty,-4) ).\n(type your answer in interval notation.)\nthe function is decreasing on the interval \n(type your answer in interval notation.)

for the quadratic function ( f(x)=-x^{2}-8x ), answer parts (a) through (f)\na. the ( y )-intercept is 0\n(type an integer or a simplified fraction.)\nb. there is no ( y )-intercept.\nwhat is the ( x )-intercept? select the correct choice below and, if necessary, fill in the answer box \ncomplete your choice\na. the ( x )-intercept(s) is/are ( -8,0 )\n(type an integer or a simplified fraction. use a comma to separate answers as needed )\nb. there is/are no ( x )-intercept(s)\n(c) use parts (a) and (b) to graph the function.\nuse the graphing tool to graph the function.\n(d) find the domain and the range of the quadratic function.\nthe domain of ( f ) is ( (-infty,infty) ).\n(type your answer in interval notation.)\nthe range of ( f ) is ( (-infty,16 ).\n(type your answer in interval notation )\n(e) determine where the quadratic function is increasing and where it is decreasing.\nthe function is increasing on the interval ( (-infty,-4) ).\n(type your answer in interval notation.)\nthe function is decreasing on the interval \n(type your answer in interval notation.)

Answer

Explanation:

Step1: Find the vertex of the quadratic function

For a quadratic function (y = ax^{2}+bx + c), the (x)-coordinate of the vertex is (x=-\frac{b}{2a}). For (f(x)=-x^{2}-8x), where (a=-1) and (b = - 8), then (x=-\frac{-8}{2\times(-1)}=-4). Substitute (x = - 4) into (f(x)): (f(-4)=-(-4)^{2}-8\times(-4)=-16 + 32=16). The vertex is ((-4,16)). Since (a=-1<0), the parabola opens down - ward.

Step2: Determine the decreasing interval

A parabola (y = ax^{2}+bx + c) ((a<0)) is increasing on ((-\infty,-\frac{b}{2a})) and decreasing on ((-\frac{b}{2a},\infty)) Since (x =-\frac{b}{2a}=-4) and (a=-1<0)

Answer:

The function is decreasing on the interval ((-4,\infty))