Question

The function h(x) = 1/2 (x+3)2 +2. How is the graph of the h(x) translated from the parent graph of a quadratic function, F(x) =x2 Select all that apply

Answer 1

For this case, the parent function is given by:
 $F (x) = x ^ 2$
 We apply the following function transformation:
 Vertical compressions:
 To graph y = a * f (x)
 If 0 <a <1, the graph of y = f (x) is compressed vertically by a factor a. (Shrinks)
 We have then:
 $y = (1/2) * x ^ 2$
 Horizontal translations:
 Suppose that h> 0
 To graph y = f (x + h), move the graph of h units to the left.
 We have then:
 $y = (1/2) * (x + 3) ^ 2$
 Vertical translations:
 Suppose that k> 0
 To graph y = f (x) + k, move the graph of k units up.
 We have then:
 $h (x) = (1/2) * (x + 3) ^ 2 + 2$
 Answer:
 Vertical compression by factor of 1/2. Horizontal displacement 3 units to the left. Vertical displacement 2 units up.