Question

Assuming the graph of y=5-x2 is given, find the equation of the graph which could be drawn in order to solve 9+4x-2x2=0

Answer 1

Often you can draw two graphs and find their intersection to correspond with another equation

For 9+4x-2x^2 = 0 this is the same as 5 - x^2 - g(x) = 0. So find the g(x) needed and this makes 5 -x^2 = g(x) and then the intersections are the solutions.

here you have y = 5 - x^2 (i)
How does it compare to y = 9+4x-2x^2? (ii)
g(x) = 5 -x^2 - (9+4x -2x^2) = -4 -4x + x^2 = (x-2)^2 - 8

So draw (x-2)^2 - 8 and y = 5 - x^2 on same axes and see where they meet I'm guessing.

Answer 2

hm ok it sort of goes along the same direction as i went :d i'll try it out thanks!