Given are the equations f(x)= -3(x+1)^2 + 12 and g(x)=14-(√3-2x).

a. *Give a window setting where you can read the points of intersections in the graph of g can read with the axis* (I use a TI-8 Plus CE-T graphing calculator and normally use the zstandard option to fit my graph, but I'm not really sure if it shows everything of the graph)

b. Calculate the coordinates of the points of intersections of both graphs. Give the answers rounded to two decimals places

Guest Feb 20, 2020

#1**+1 **

Well....I don't know if this helps but.....here's a graph with the intersection points shown :

https://www.desmos.com/calculator/o3gydmyzdf

CPhill Feb 20, 2020

#3**+1 **

We have

y = -3 ( x + 1)^2 + 12

y = 14 - √(3 -2x]

Setting these equal we have that

-3 ( x + 1)^2 + 12 = 14 - √[3-2x]

-3x^2 -6x -3 + 12 = 14 - √[3-2x]

-3x^2 -6x + 9 = 14 - √[3-2x]

-3x^2 - 6x - 5 = -√[3-2x] multiply through by -1

3x^2 + 6x + 5 = √[3-2x]

This would be* very *dfficult to solve algebraically

Here's a graph of both sides of the equation with the intersection points shown :

https://www.desmos.com/calculator/fsjl5mhaqo

Remember to round these to two decimal places....

CPhill Feb 20, 2020

#4**+1 **

Thank you! So solving it algebraically would give me the points of intersection? The assignments asks for me to show my calculation but if it is that difficult i might just skip it then.

Guest Feb 20, 2020

#5**+1 **

The calculation of these solutions algebraically is above my pay-grade.....LOL!!!!

WolframAlpha shows the * exact* solutions here :

https://www.wolframalpha.com/input/?i=-3+%28+x+%2B+1%29%5E2++%2B+12++%3D++14+-+%E2%88%9A%5B3-2x%5D

As you can see.....these are really "messy "

A graph seems the way to go.....!!!!

CPhill
Feb 20, 2020