MATH SOLVE

7 months ago

Q:
# 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

Accepted Solution

A:

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

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