Respuesta :
Answer:
[tex]V(-5,8)[/tex]
Step-by-step explanation:
The given function is
[tex]y=x^{2}[/tex]
Notice that this is a parent function, that is, the simplest form of a quadratic function.
The transformations are:
- 5 units to the left.
- 8 units up.
Notice that this are rigid transformations, specifically, they are translations only.
Remeber, to move a function to the left, we must sum units to the x-variable. To move a function upwards, we must sum units to the y-variable.
Therefore, the transformed function is
[tex]y=(x+5)^{2} +8[/tex]
Notice that the equation has the form [tex]y=a(x-h)^{2} +k[/tex].
Where [tex]a=1[/tex], [tex]h=-5[/tex] and [tex]k=8[/tex].
Additionally, an important property of quadratic function is the vertex of the parabola which represents the function, which is at [tex]V(h,k).[/tex]
Therefore, in this case, the vertex is at [tex]V(-5,8)[/tex]
