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
+128474 Well....I don't know if this helps but.....here's a graph with the intersection points shown :
https://www.desmos.com/calculator/o3gydmyzdf
+128474 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....
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.
+128474 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.....!!!!
