Answer:
(a) --> f(x) = -(x - 4)²
(b) --> f(x) = x² + 3
(c) --> f(x) = (x - 2)²
(d) --> 6. f(x) = 3 - x²
Parent function of all the graphs is y = x²
(a)
The graph makes a sad face meaning the coefficient will be negative.
Comparing to the parent function y = x², the graph has been translated 4 units to the right.
Equation: f(x) = -(x - 4)²
(b)
The graph makes a happy face meaning the coefficient will be positive.
Comparing to the parent function y = x², the graph has been translated 3 units up.
Equation: f(x) = x² + 3
(c)
The graph makes a happy face with translation 2 units to the right.
Equation: f(x) = (x - 2)²
(d)
The graph makes a sad face with translation 3 units up across y axis.
Equation: f(x) = -x² + 3
Translation rules:
f(x + a) : translation a units left in the x axis.
f(x - a) : translation a units right in the x axis.
f(x) + b : translation b units up in the y axis.
f(x) - b : translation b units down in the y axis.