Write the formula for the parabola that has x- intercepts (5+ sqrt3 ,0) and (5− sqrt 3 ,0), and y- intercept (0,4)
+23245 An equation for a parabola is y = a(x - r)(x -s) where r and s are x-intercepts.
Placing the two intercepts into this formula, we get: y = a( x - (5 + sqrt(3) )( x - (5 - sqrt(3) )
---> y = a( x - 5 - sqrt(3) )( x - 5 + sqrt(3) )
y = a(x2 - 10x + 22)
Since the point (0, 4) is on this parabola:
4 = a(02 -10·0 + 22)
4 = 22a
a = 2/11
y = (2/11)(x2 - 10x + 22)
