Given the parent function f(x)=x^2, write the equation in 3 different forms, that would result in the graph below.


a) In Vertex form: _
b) In Standard form: _
c) In Factored form: _

Step-by-step explanation:

f(x)=a(x-3)(x-5)

∵ (4,-1 ) lies on it.

-1=a(4-3)(4-5)

-1=a×1×-1

-a=-1

a=1

f(x)=(x-3)(x-5)    factored form

f(x)=x²-3x-5x+15

f(x)=x²-8x+15     standard form

f(x)=x²-8x+15

add and subtract (-8/2)² or 16

f(x)=x²-8x+16-16+15

or f(x)=(x-4)²-1   vertex form

f(x)