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oh yeah but how do we find the x intercepts of that inverse function?
and how come there's a negative sign here => -(x-7)
the x-intercept is the point such that it hits the x axis which is the line where y=0 so to find the x-intercept of g^-1 we set y=g^-1 and solve y = 1 +- sqrt((7 - x)/2) 0 = 1+- sqrt((7 - x)/2) -1 = +- sqrt((7 - x)/2) 1 = (7 - x)/2 2 = 7 - x -5 = -x x = 5 so the x-intercept is (5, 0) the reason there is a negative in that step before the (x - 7) is because i divided by -2 and transferred that negative to the numerator because it's standard for the denominator to be positive
thank you very much
and how do we find the vertex of it?
of g^-1? well, i'd put it into horizontal parabola vertex form: x = a(y - h)^2 + k so x = -2(y - 1)^2 + 7 this makes it easy to find the vertex, which is (h,k). if you look at the equation, we see h = 1 and k = 7 so the vertex of g^-1 is (1,7)
the vertex is in the exact spot as the original equation but not the inverse function >_>
yeah sorry my bad the vertex is actually (k,h) for horizontal. if you rewrite the vertex form as: x - k = a(y - h)^2 you just look at which is subtracted from what variable to determine what coordinate it designates for the vertex. since it's (k,h) you should have (7,1). my bad
the vertex coordinates swap between g and g^-1 which makes sense because you're swapping the x,y values
ohh i see
but for the x intercept im supposed to also have 2 coordinates is 5,0 one of them?