The translations of the graph of the parent function [tex]f(x) = x^2[/tex] that result in the graph of [tex]g(x) = (x + 2)^2 + 6[/tex] will be that the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
What is translations ?
Translation is the act or process of changing completely. In this also the graph changes or transform. i.e. in the graph values of the expression are changing and forming new shape.
We have,
Parent Quadratic equation [tex]f(x) = x^2[/tex]
And,
Translation of graph [tex]g(x) = (x + 2)^2 + 6[/tex]
So,
Parent quadratic function works in the form of [tex]f(x) = a(x-h)^2 + k[/tex]
Here,
"h" tells if the vertex of the parabola is going left or right.
"k" determines if the vertex of the parabola is going up or down.
So, According to the question;
We have,
Translation of graph [tex]g(x) = (x + 2)^2 + 6[/tex]
So,
From equation we find out that the vertex of the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
(Always remember if moving left means sign would be of plus because in parent quadratic function is in the form of [tex]f(x) = a(x-h)^2 + k[/tex] we have minus sign in it.)
Hence, we can say that the Translation of the graph of the parent function [tex]f(x) = x^2[/tex] that result in the graph of [tex]g(x) = (x + 2)^2 + 6[/tex] will be that the parabola moved [tex]2[/tex] units to the left and [tex]6[/tex] units up.
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