D. F(x)= (x-1)^2+3
This is the equation of a vertical parabola open upward
The vertex is a minimum
The vertex is the point (0,0)
The graph of f(x) has the same shape as the graph of g(x), but is shifted up 1 unit
The vertex of the function f(x) is (0,1)
The rule of the translation of g(x) to f(x) is
(x,y) ----> (x,y+1)
The equation of f(x) is equal to
The graph of F(x) is a translation of the graph of G(x) by 4 units down and 3 units right.
4 units down is the vertical shift. Vertical shift is obtained by adding or subtracting a number from the function value. Subtraction indicates a downward shift and addition indicates an upward shift. Since the graph is shifted 4 units down, the new equation after this translation will be:
3 units to the right is the horizontal shift. Horizontal shift is obtained by adding or subtracting a number from x. Subtraction indicates a shift towards right and addition indicates a shift towards left. Since the graph is being shifted 3 units to right, the new equation after this transformation will be:
with that template in mind, let's see
down by 5 units, D = -5
to the left by 4 units, C = +4
A. Takes it 1 to the right and 3 up
To translate a graph right you -3 from x. To translate a graph up you +4.
The equation is y = a(b(x-c))+d
So for it to move right three units, it would be x - 3.
For it to move up 4 unites, it would be x+4.
So the equation would be y = (x - 3)^2 + 4
The parent function is .
This function has its vertex at the origin (0,0).
When this function is shifted down 5 units and to the left 4 units, then its new vertex will be at (-4,-5)
The vertex form of the equation is given by;
where (h,k)=(-4,-5) is the vertex and a=1 because of the parent function.
Hence its equation is
f(x) = (x+1)^2
Function transformations move a graph by shifting it up or down or left or right as well as vertically or horizontally stretching it. They take the parent function and manipulate the equation to create a new graph. The parent graph here is x^2 and its shifts 1 unit to the left. Horizontal shifts occur within the operation such as (x+/-a)^2. Here it would be (x+1)^2 since it moved 1 unit to the left. Left is addition and subtraction is right.
A function g(x) = x² has been given as the parent function.
This function then shifted 5 units down.
Translated function formed will be f(x) = x² - 5
Further this graph has been shifted 4 units to the left then the function will become
f(x) = [x - (-4)]² - 5
f(x) = (x + 4)² - 5
Therefore, option C is the answer.