Suppose a parabola has an axis of symmetry at x=8 a maximum height of 1 and also passes through the point (9, –1). Write the equation of the parabola in vertex form.
The vertex form of a parabola is given by the equation:
y = a(x-h)^2 + k,
where (h, k) represents the coordinates of the vertex.
Given that the axis of symmetry is at x = 8, it means that the vertex is located at (8, k). Since the maximum height is 1, the k value must be equal to 1.
So the equation in vertex form becomes:
y = a(x-8)^2 + 1.
Now we need to find the value of 'a'.
Since the parabola also passes through the point (9, -1), we can substitute this point's coordinates into the equation to solve for 'a'.
-1 = a(9-8)^2 + 1
-1 = a(1)^2 + 1
-1 = a + 1
a = -2
Substituting a = -2 into the equation, we get the final equation of the parabola in vertex form:
y = -2(x-8)^2 + 1