Factors of the function f ( x ) are:
f ( x ) = ( x + 5 ) ( x - 3 ) = x² - 3 x + 5 x - 15 = x² + 2 x - 15
x - intercepts of this function are - 5 and 3.
f ( x + 2 ) = ( x + 2 )²+ 2 ( x + 2 ) - 15 = x² + 4 x + 4 + 2 x + 4 - 15 =
= x² + 6 x - 7
x² + 6 x - 7 = x² + 7 x - x - 7 = x ( x + 7 ) - ( x + 7 ) = ( x + 7 ) ( x - 1 )
Answer : the x - intercepts of the graph f ( x + 2 ) are - 7 and 1.
