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Oct 16, 2018

#1
+103148
+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

Oct 16, 2018
#2
+1

Thank you so much for your help! Have a wonderful day/night!

Guest Oct 16, 2018