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).
Step-by-step explanation:
Figure represents graph of [tex]f(x) = x^{2}[/tex] and [tex]g(x) = (x-2)^{2} -3[/tex]
Here, [tex]f(x) = x^{2}[/tex] is " Translated " or " Transformation " to [tex]g(x) = (x-2)^{2} -3[/tex]
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, [tex]g(x) = (x-2)^{2} -3[/tex] = f(x-2) + (-3)
Therefore, new vertex we get is (2,-3)
Also, [tex]g(x) = (x-2)^{2} -3[/tex]
[tex]g(0) = (0-2)^{2} -3[/tex]
[tex]g(0) = (4} -3[/tex]
[tex]g(0) = 1 [/tex]
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).
