Respuesta :
Solution
Write your answer in the form a(x–h)2+k, where a, h, and k are integers.
Step-by-step explanation:
Given:
The function
[tex]f(x)=x^2[/tex]A standard parabola with vertex at origin is represented as:
[tex]f(x)=ax^2[/tex]The above function is a standard parabola with vertex at origin and opening upward.
The vertex of the above function is at the origin ( 0 , 0) and the value of is 1.
Now, the function is translated 2 units left
So, from the rule of function transformations, if a graph is moved up by units, then units is added to the function.
Therefore,
[tex]\begin{gathered} g(x)=f(x)-2 \\ g(x)=x^2-2 \end{gathered}[/tex]Also, the vertex of f(x) will be translated 2 units left. So, the co-ordinates of the vertex of g(x) will be (0 , 0-2) = (0,-2)
Now, express the above function in the vertex form
[tex]g(x)=a(x-h)^2+k[/tex]now we have a = 1, h = 0, k = -2
This gives
[tex]g(x)=1(x-0)^2-2[/tex]