Question

The graph of f(x) = x2 is translated to form

g(x) = (x – 2)2 – 3.

On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4).

Which graph represents g(x)?

On a coordinate plane, a parabola opens up. It goes through (0, 1), has a vertex at (2, negative 3), and goes through (4, 1).
On a coordinate plane, a parabola opens up. It goes through (negative 3, 4), has a vertex at (negative 2, 3), and goes through (negative 1, 4).
On a coordinate plane, a parabola opens up. It goes through (1, 4), has a vertex at (2, 3), and goes through (3, 4).
On a coordinate plane, a parabola opens up. It goes through (negative 4, 1), has a vertex at (negative 2, negative 3), and goes through (0, 1).

Answer 1

Graph A is the correct answer

Explanation:

I juust took the test and got it right :D hope this helps

Answer 2

The correct answer is: A,

On a coordinate plane, a parabola opens up. It goes through (0, 1), has a vertex at (2, negative 3), and goes through (4, 1).

Explanation:

Figure represents graph of
`f(x) = x^(2)` and
`g(x) = (x-2)^(2) -3`

Here,
`f(x) = x^(2)` is " Translated " or " Transformation " to
`g(x) = (x-2)^(2) -3`

In process of transformation,

You should remember that shape of curve remain same and only changes we get in vertex shift

Now, Vertex can be shift in two direction, we are going to discuss both the cases

(A). Shifting of Vertex in X-Axis:

A new function g(x) = f(x - c) represents to X-axis shift and In graph of f(x), Curve is shifted c units along right side of the X-axis

(B). Shifting of Vertex in Y-axis:

A new function g(x) = f(x) + b represents to Y-axis shift and In graph of f(x), Curve is shifted b units along the upward direction of Y-axis

Looking at the figure, You can see that vertex of f(x) is shifted 2 Units in X-axis and Negative 3 units in Y-axis and result into g(x)

Now,
`g(x) = (x-2)^(2) -3` = f(x-2) + (-3)

Therefore, new vertex we get is (2,-3)

Also,
`g(x) = (x-2)^(2) -3`

`g(0) = (0-2)^(2) -3`

`g(0) = (4} -3`

`g(0) = 1`

So. g(x) passes through (0,1)

The correct answer is: A On a coordinate plane, a parabola opens up. It goes through (0, 1), has a vertex at (2, negative 3), and goes through (4, 1).