Mohamed_raway math

Question

If the curve of the quadratic function f(x) is symmetric in the interval [-2,4] and f (a) = f(a+2) , then a = ....

( 1 ,-2 , 7 , 4 )

Answer 1

symmetric in the interval [-2,4] means an axis of symmetry x= 1

as |-2-1|=3 = |4-1|

y = a(x-1)^2 + h is an upward opening parabola with vertex (1,h) and axis of symmetry x=1

f(a) = f(a+2) means two points (a,f(a)) and (a+2,f(a+2)) each symmetric about x=1

|a-1|= |a+2-1|

|a-1|=|a+1|

a-1 =-a-1

2a = 0

a = 0