Final answer:
To find the vertex of a quadratic function, use the vertex formula h = -b/(2a) for the x-coordinate, and then plug this into the function to find the y-coordinate, giving the vertex (h, k). This is different from using the quadratic formula, which finds the roots of the equation.
Step-by-step explanation:
To find the vertex of a quadratic function f(x) using the vertex formula, we need to identify the equation of the form ax²+bx+c. The vertex form of a quadratic equation is y = a(x-h)² + k, where (h,k) is the vertex of the parabola. For a given quadratic equation in the form ax²+bx+c = 0, the vertex (h, k) can be found using the formula h = -b/(2a) and then evaluating f(h) to find k.
Another way to solve the quadratic equation is by using the quadratic formula to find the x-values of the roots, although that does not directly give the vertex. If necessary, you can then use the x-values of the roots to find the x-value of the vertex as the midpoint between the roots for a parabola opening upwards or downwards.