Weare given the quadratic function of the form: F(x) = x^2 + 5 , and are asked to shift the graph of this function 3 units to the left.
We recall the definition of horizontal shifts for the graph of a function, and type the following transformation adding 3 units explicitely to the variable "x" as shown below;
f (x) = (x + 3)^2 + 5
Since we are asked to now write the transformation in "standard form", we solve the square of the binomial in parenthesis:
f(x) = x*2 + 6 x + 9 + 5
f(x) = x^2 + 6 x + 14
This is the standard form of the transformed function.
Would you like to see the graph of the original and of the transformed functions to corroborate the shift to the left?
The following images show the actual shift to the left in three units:
The curve in blue is that of the function f(x) = x^2 + 5
and te curve in orange is that of the transformed function f(x) = x^2 + 6x + 14.
We see the clear shift of the vertex that moved to the left in 3 units.
