The function gets shifted toward the left when 3 is added in a variable and it gets shifted downward when subtracting 3 in a function. the vertex of the function is on (-3, -3).
The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Given
The function is
[tex]\rm f(x) = \dfrac{1}{2} x^2 + 3x + \dfrac{3}{2}[/tex]
Take 1/2 common,
[tex]\rm f(x) = \dfrac{1}{2}( x^2 + 6x + 3)[/tex]
Add and subtract 9.
[tex]\rm f(x) = \dfrac{1}{2}( x^2 + 6x + +9- 9 + 3)\\\\\rm f(x) = \dfrac{1}{2}[(x + 3 ^2 - 6)]\\\\\rm f(x) = \dfrac{1}{2}(x+ 3)^2 - \dfrac{6}{2}\\\\\rm f(x) = \dfrac{1}{2}(x+ 3)^2 - 3[/tex]
We know that if 3 is added in a variable it gets shifted toward the left.
And if we subtract 3 in a function then it gets shifted downward.
Thus, the vertex of the function is on (-3, -3).
More about the function link is given below.
https://brainly.com/question/5245372
