Answer:
1) Identify the values of a, b and c in the function [tex]f(x) = ax ^ 2 + bx + c[/tex]
2) Do [tex]x = -\frac{b}{2a}[/tex]
[tex]y = f(-\frac{b}{2a})[/tex]
3) Then [tex]h = x[/tex] and [tex]k = y[/tex]
4) Once found the values of h and k, write the equation as:
[tex]f(x) = (x-h) ^ 2 + k[/tex]
Step-by-step explanation:
The standard form of a quadratic function is:
[tex]f(x) = ax ^ 2 + bx + c[/tex]
Where a, b and c are the coefficients of the monomials, and they are real numbers. By definition, the vertex of this function is:
[tex](-\frac{b}{2a}, f(-\frac{b}{2a}))[/tex]
Then, the vertex form of a quadratic function is:
[tex]f(x) = (x-h) ^ 2 + k[/tex]
Where the point (h, k) represents the vertex of the function.
The steps to convert a quadratic function to the standard form the vertex form is:
1) Identify the values of a, b and c in the function [tex]f(x) = ax ^ 2 + bx + c[/tex]
2) Do [tex]x = -\frac{b}{2a}[/tex]
[tex]y = f(-\frac{b}{2a})[/tex]
3) Then [tex]h = x[/tex] and [tex]k = y[/tex]
4) Once found the values of h and k, write the equation as:
[tex]f(x) = (x-h) ^ 2 + k[/tex]
