Final answer:
To find the general form of a quadratic equation given the vertex (2,5) and a point (-4,3), use the vertex form equation to solve for 'a', then expand and simplify to get the equation in general form.
Step-by-step explanation:
To find the general form of the equation of a quadratic function given a vertex (h,k) and a point on the graph (x,y), we use the vertex form of a quadratic equation, which is y = a(x - h)² + k, where a is a coefficient that affects the width and direction of the parabola.
With the vertex at (2,5), the equation becomes y = a(x - 2)² + 5. Now, we'll plug in the coordinates of the given point (-4,3) to solve for a. Substituting x with -4 and y with 3, we get 3 = a(-4 - 2)² + 5. Simplifying, 3 = a(36) + 5. To solve for a, subtract 5 from both sides and then divide by 36, resulting in a = -1/18.
Substitute a back into the vertex form to get the quadratic equation in vertex form: y = (-1/18)(x - 2)² + 5. To convert this into the general form ax² + bx + c, expand the equation and simplify.