To convert the quadratic function from standard form to vertex form, we can complete the square. The function given is:
f(x) = x² – 6x + 3
First, we focus on the x² and -6x terms. To complete the square, we take the coefficient of x (which is -6), divide it by 2 (giving us -3), and then square it to find the value to add and subtract. So:
(-3)² = 9
Now we rewrite the function by adding and subtracting 9:
f(x) = (x² – 6x + 9) – 9 + 3
Now we can rewrite the trinomial as a squared term:
f(x) = (x – 3)² – 6
Now we have the function in vertex form:
f(x) = (x – 3)² – 6
The vertex of this parabola is at the point (3, -6). Therefore, the equivalent function in vertex form is f(x) = (x – 3)² – 6.