Question

The vertex of the parabola is at the point (2,4), and the point (3,6) is on the parabola. What is the equation of the parabola?

Answer 1

We know that for the parent function
y = x²
when x=1, the value of y is also 1.
That is, when the horizontal distance from the vertex is 1, the vertical distance is also 1.
In your parabola, the point (3, 6) has a horizontal distance of 1 from the vertex (2, 4), but a vertical distance of 2. That means the vertical scale factor is 2, and the translated parabola's equation is ...
B. y = 2(x - 2)² + 4