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Please help! I'm confused. Please show work because I want to know how to solve these. Thanks!!

Guest Oct 16, 2018

#1**+2 **

f(x) = -x^2 -2x + 8

This is a parabola that turns "downward" because thw leading coefficient is negative

To find the x coordinate of the vertex...

In the form ax^2 + bx + c

The x coordinate of the vertex is -b / [ 2a ]

So....in our function, b = (-2) and a = (-1)

So... -b / [ 2a] = 2 / [ 2 * -1 ] = 2 / -2 = -1

To find the associated y value for the function....put -1 back into it and evaluate

- (-1)^2 -2(-1) + 8 = -1 + 2 + 8 = 9

So...(-1,9) is the "high point" of the function

So....this function will increase from (-infinity, to -1)

To find out where it tis positive on this interval...we can find the root on this side [ where it crosses the x axis]

So...we want to solve

-x^2 - 2x + 8 =0 multiply through by -1

x^2 + 2x - 8 = 0 factor

(x + 4) (x - 2) =0

Set each factor to 0 and solve for x and we get x = - 4 or x = 2

So....this tells us that the function is positive and increasing from

-4 < x < -1 ⇒ B

Here is the graph : https://www.desmos.com/calculator/lmmko24qwo

CPhill Oct 16, 2018