find the x-intercepts of the parabola with vertex(6,27) and y-intercept (0,-81). write answer in form (x1,y1)(x2,y2). if necessary ,round to the nearest hundredth .
The vertex form of the equation is: y = a ( x - h )² + k - 81 = a ( 0 - 6 )² + 27 - 81 = 36 a + 27 - 108 = 36 a a = - 108 : 36 a = - 3 y = - 3 ( x - 6 )² + 27 y = - 3 ( x² - 12 x + 36 ) + 27 y = - 3 x² + 36 x - 108 + 27 y = - 3 x² + 36 x - 81 y = - 3 ( x² - 12 x + 27 ) x² - 12 x + 27 = 0 x² - 9 x - 3 x + 27 = 0 x ( x - 9 ) - 3 ( x - 9 ) = 0 ( x - 9 ) ( x - 3 ) = 0 x 1 = 3, x 2 = 9 Answer: The x-intercepts are ( 3, 0 ) and ( 9, 0 ).
