Final answer:
To find the vertex form of a quadratic equation, calculate the roots using the quadratic formula, and then find the vertex (h, k) through substitution to write the equation in vertex form (a(t - h)² + k).
Step-by-step explanation:
To find the vertex form of a quadratic equation using a calculator, you must first have the standard form of the quadratic equation, which is at² + bt + c = 0. For example, if you are given the equation 4.90t² - 14.3t - 20.0 = 0, you will utilize the quadratic formula, which is (-b ± √(b² - 4ac)) / (2a), to find the roots of the quadratic equation. After finding the roots, you can then use them to write the vertex form of the quadratic, which is a(t - h)² + k, where (h, k) is the vertex of the parabola.
The h value is computed from (-b / (2a)), and the k value is the function value at the vertex, which can be found by substituting h back into the original equation. In this example, first calculate the root using the quadratic formula and rounding to four decimal places if necessary. Then substitute to find k.