Question

The graph of the function g(x) = x2 + 3x - 4 is shifted 5 units to the left. Plot the zeros of the new function on the provided graph. Drawing Tools Select Point ResetUndoDelete

Answer 1

Horizontal translations
 Suppose that h> 0
 To graph y = f (x + h), move the graph of h units to the left.
 We have then:
 g (x + 5) = (x + 5) 2 + 3 (x + 5) - 4
 Rewriting we have:
 f (x) = x ^ 2 + 10x + 25 + 3x + 15 - 4
 f (x) = x ^ 2 + 13x + 36
 Equaling zero we have:
 x ^ 2 + 13x + 36 = 0
 We look for the roots of the polynomial:
 (x + 9) (x + 4) = 0
 x1 = -9
 x2 = -4
 Answer:
 The zeros of the new function are:
 x1 = -9
 x2 = -4