FIND THE COORDINATES OF THE VERTEX FOR y fx 2 x 52 7 FIN

FIND THE COORDINATES OF THE VERTEX FOR y = f(x) = -2 (x - 5)^2 - 7 FIND THE MAXIMUM VALUE OF THE FUNCTION f(x) = -4x^2 - 12x + 15.

f(x)=-2(x-5)^2-7

comparing it with the equation of parabola which is

y=a(x-h)^2 + k

we get h=5 and k =-7

Therefore centre is at(5,-7)

b. f(x)= -4x^2 -12x+15

the given function is maximum at its vertex

And vertex,x=-b/2a= -(-12)/2(-4)=12/-8=-1.5

f(-1.5)= -4(-1.5)^2 -12(-1.5)+12= -9 +18+12=21

therefore maximum value is 21