Graph the quadratic function f(x) = - 4x - 40x -84. Give the (a) vertex, (b) axis,(c) domain, and (d) range. Then determine (e) the largest open interval of thedomain over which the function is increasing and (f) the largest open interval overwhich the function is decreasing(a) The vertex is(Type an ordered pair.)

Answered: Graph the quadratic function f(x) = -…

Advanced Engineering Mathematics

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Author:Erwin Kreyszig

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Graph the quadratic function f(x) = - 4x - 40x -84. Give the (a) vertex, (b) axis,
(c) domain, and (d) range. Then determine (e) the largest open interval of the
domain over which the function is increasing and (f) the largest open interval over
which the function is decreasing
(a) The vertex is
(Type an ordered pair.)

Expert Solution

Step 1

The given function can also be written as $f (x) - 16 = - 4 {(x + 5)}^{2}$ . This equation is similar to the general equation of a parabola. Therefore, comparing it with the general equation of the parabola $(y - y_{1}) = 4 a (x - x$ ₁)2, we get that the vertex of this function is $(- 5, 16)$ .

Comparing the above equation with the general equation of the parabola, we get the axis of the parabola as the line $x = - 5$ .

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