Question

n two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = (x+1)2. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answer 1

x-intercept of f(x) is 0

x-intercept of g(x) is -1.g(x) comes from the base function f(x) when it moves 1 unit to left.

Explanation:

We have given two graphes.

We have to compare the x-intercept of the graphes.

As f(x) = x²

And g(x) = (x+1)²

put f(x)= 0 we have,

f(x) = x² = 0

x=0 (x-intercept)

Put g(x) = 0 then,

g(x) = (x+1)² = 0

(x+1) = 0

x= -1 (x-intercept)

The vertex of the parabola f(x) is (0,0).

And the vertex of parabola g(x) is (-1,0).

g(x) comes from the base function f(x) when it moves 1 unit to left.

Answer 2

x-intercept of f(x) is 0

x-intercept of g(x) is -1

g(x) is the image of f(x) after translate it 1 unit to the left

Explanation:

In the graph f(x) = x²

The x-intercept = 0 ⇒ ∵ f(x) = 0 ⇒ ∴ x² = 0 ⇒ x = 0

The vertex of the parabola is (0 , 0)

In the graph g(x) = (x + 1)²

The x-intercept = 0 ⇒ ∵ g(x) = 0 ⇒ ∴ (x + 1)² = 0

x + 1 = 0 ⇒ x = -1

The vertex of the parabola is (-1 , 0)

∴ g(x) is the image of f(x) after translate it 1 unit to the left