Question

The equation of a parabola in vertex form is given by: y = a(x-h)^2 + k, where (h, k) is the vertex. In this case, the vertex is (0, 3) and you have another point (1, -4). You can use this information to find 'a' and write the equation.

Plug in the values of the vertex (0, 3) into the equation: 3 = a(0 - 0)^2 + 3.
Use the other point (1, -4) to solve for 'a': -4 = a(1 - 0)^2 + 3.
Solve for 'a': -4 = a + 3, a = -7.
Write the equation with the vertex and 'a': y = -7x^2 + 3.

Answer 1

To determine the coefficient 'a' for the parabola's equation, the vertex (0, 3) and the point (1, -4) are used. By substituting these into the standard vertex form equation y = a(x-h)^2 + k, we find that a = -7, leading to the full equation of the parabola: y = -7x^2 + 3.

Step-by-step explanation:

To find the coefficient 'a' for the equation of a parabola, we can use the vertex form of the equation y = a(x-h)^2 + k, where (h, k) is the vertex. Since the vertex is given as (0, 3), we can substitute these values into the equation to get 3 = a(0-0)^2 + 3, which simplifies to 3 = 3. This confirms that the vertex has been correctly identified, but it doesn't help us find 'a'. To solve for 'a', we use the other given point (1, -4). Plugging these values into the vertex form gives us -4 = a(1-0)^2 + 3. Simplifying this equation yields -4 = a + 3. Subtract 3 from both sides to get a = -7. Therefore, the complete equation of the parabola is y = -7x^2 + 3.