Given the vertex ( 4, 6 )and the point(1, -3), write the vertex form equation of the quadratic function.

Step-by-step explanation:

A given quadratic has its vertex at (4, 6) and the point (1, -3). We want to write the equation in vertex form of the quadratic.

Recall that vertex form is given by:

Where (h, k) is the vertex and a is the leading coefficient.

Since our vertex is at (4, 6), h = 4 and k = 6:

To determine the leading coefficient, since we are given that (1, -3) is a point on the parabola, when x = 1, y = -3. Substitute and solve for a:

Hence, the leading coefficient a is -1.

Then our equation in vertex form is: