Question

Given a vertex and point on a quadratic, how could you find the equation of the function?

Answer 1

To find the equation of a quadratic function given a vertex and a point, use the vertex form of a quadratic equation, substitute the given values to solve for the coefficient 'a', and then write the complete equation.

Step-by-step explanation:

To find the equation of a quadratic function given the vertex and a point, we start by using the vertex form of a quadratic equation: y = a(x - h)2 + k, where (h, k) is the vertex of the parabola. Suppose the vertex is (h, k) and the given point is (x_1, y_1). We substitute these values into the vertex form to find the value of a:

• y_1 = a(x_1 - h)2 + k

Then we solve for a. Once we have a, we'll have the complete equation of the quadratic function. For example, if the quadratic is in the form at2 + bt + c = 0, and you are given that a = 4.90, b = 14.3, and c = -20.0, you could use the quadratic formula to find solutions for t.

However, to construct the equation from a vertex and a point, you would not typically use these constants directly unless they relate to the vertex and point in question.