Suppose a parabola has an axis of symmetry at x=−8 a maximum height of 2, and passes through the point (−7,−1). Write the equation of the parabola in vertex form.(1 point)
The vertex form of a parabola is given by the equation: y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Since the axis of symmetry is at x = -8, the vertex has x-coordinate -8. Therefore, h = -8.
The parabola has a maximum height of 2, which means the vertex has a y-coordinate of 2. Therefore, k = 2.
Using the vertex form, the equation of the parabola is: y = a(x-(-8))^2 + 2.
Simplifying further: y = a(x+8)^2 + 2.
To find the value of "a", we can substitute the coordinates of the point (-7, -1) into the equation and solve for "a".
-1 = a((-7)+8)^2 + 2
-1 = a(1)^2 + 2
-1 = a + 2
a + 2 = -1
a = -3
Therefore, the equation of the parabola in vertex form is: y = -3(x+8)^2 + 2.