suppose a pararbola has an axis of symmetry at x = -1, a maximum height of 6, and passes through the point ( -2, 1). Write the equation of the parabola in vertex form.
The vertex form of the equation of a parabola is given by:
y = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola.
We are given that the axis of symmetry is x = -1, which tells us the x-coordinate of the vertex is -1. Therefore, h = -1.
We are also given that the maximum height of the parabola is 6. Since the vertex is at height k, we can substitute k with 6.
So far, we have: y = a(x - (-1))^2 + 6
Simplifying: y = a(x + 1)^2 + 6
Finally, we know that the parabola passes through the point (-2, 1). We can substitute these coordinates into the equation to solve for a.
1 = a((-2) + 1)^2 + 6
1 = a(1)^2 + 6
1 = a + 6
a = -5
Substituting the value of a into the equation, we get:
y = -5(x + 1)^2 + 6
Therefore, the equation of the parabola in vertex form is y = -5(x + 1)^2 + 6.