Question

find the x-intercept of the parabola with vertex (4,-1) and y- intercept (0,15). write answer in (x1,y1) (x2,y2) form :D ...?

Answer 1

Vertex form of the equation:
y = a ( x - h )² + k;
15 = a ( 0 - 4 )² - 1
15 = 16 a - 1
16 a = 16
a = 16 : 16
a = 1
After that we have to transform the equation to the standard form:
y = ( x - 4 )² - 1
y = x² - 8 x + 16 - 1
y = x² - 8 x + 15
Finally we have to find the zeroes:
x² - 8 x + 15 = 0
x² - 5 x - 3 x + 15 = 0
x ( x - 5 ) - 3 ( x - 5 ) = 0
( x - 5 ) ( x - 3 ) = 0
x = 3, x = 5
Answer:
( x 1, y 1 ) ; ( x 2 , y 2 ) = ( 3, 0 ) ; ( 5 , 0 )