Final answer:
To find a quadratic function with given vertex and point, use the vertex form of a parabola, plug in the vertex and point to solve for 'a', and use technology like graphing calculators to simplify the process.
Step-by-step explanation:
To find a quadratic function with a given vertex and point, you can use a standard form equation of a parabola, which is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
First, substitute the vertex into the equation. Then, use the coordinates of the given point to solve for 'a'. For example, if the vertex is (3, -2) and the point is (4, 0), you would start by replacing h and k in the equation, getting y = a(x-3)^2 - 2.
Next, plug in the coordinates of the point for x and y, resulting in 0 = a(4-3)^2 - 2. Solve for 'a' to find the quadratic function. To ease the process, you can use calculators designed for graphing polynomials like the TI-83 or TI-84+, which allow for equation grapher functionalities.
When you're using technology to aid in mathematical calculations, it's essential to understand the solution of quadratic equations and how to interpret the polynomial curve on an equation grapher. The use of spreadsheets, statistical software, or graphing calculators makes it easier to solve these problems, as manually calculating can be tedious.