Final answer:
To find the formula for a parabola given its vertex and a point it passes through, we can use the vertex form of a quadratic equation. The equation of the parabola with vertex (3,10) and passing through (2,3) is y=-7(x-3)^2+10.
Step-by-step explanation:
To find the formula for a parabola given its vertex and a point it passes through, we can use the vertex form of a quadratic equation. The vertex form is y = a(x-h)^2 + k, where (h, k) represents the coordinates of the vertex.
Using the given vertex (3,10), we substitute h=3 and k=10 into the vertex form equation. So, the equation becomes y=a(x-3)^2+10.
To find the value of 'a', we substitute the coordinates of the point (2,3). So, we have 3=a(2-3)^2+10. Solving for 'a', we get a=-7.
Therefore, the equation of the parabola is y=-7(x-3)^2+10.