Final answer:
To write the equation of a parabola, use the standard form y = a(x - h)^2 + k, where (h, k) is the vertex. Substitute the given values to find the equation.
Step-by-step explanation:
To write an equation of a parabola that passes through the point (-1, 2) and has a vertex (4, -9), we need to use the vertex form of a parabolic equation, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. Here, our vertex (h, k) is (4, -9), so we plug these values into the vertex form to get y = a(x - 4)² - 9. To find the value of a, we use the point (-1, 2) that lies on the parabola. Plugging these values into the equation, we get 2 = a(-1 - 4)² - 9. Simplifying, we have 2 = a(25) - 9, which gives us 11 = 25a. Hence, a is 11/25. Therefore, the parabolic equation is y = (11/25)(x - 4)² - 9.
To write the equation of a parabola that passes through a given point and has a given vertex, we can use the standard form of the equation:
y = a(x - h)^2 + k
where (h, k) is the vertex of the parabola. Plugging in the values from the given vertex, we have:
y = a(x - 4)^2 - 9
Next, substitute the coordinates of the given point (-1, 2) into the equation:
2 = a(-1 - 4)^2 - 9
Solving for a, we get a = -1/5.
Therefore, the equation of the parabola is y = (-1/5)(x - 4)^2 - 9.