Suppose a parabola has an axis of symmetry of x=−3, a maximum height of -4, and passes through the point (-2, -6). Write the equation of the parabola in vertex form.
The equation of a parabola in vertex form is given by:
y = a(x - h)^2 + k
Where (h, k) represents the vertex of the parabola. In this case, we have the vertex form as:
y = a(x + 3)^2 - 4
Since the axis of symmetry is given by x = -3, the value of h is -3.
Now, we need to find the value of "a". We can substitute the coordinates of the given point (-2, -6) into the equation to find "a":
-6 = a(-2 + 3)^2 - 4
-6 = a(1)^2 - 4
-6 = a - 4
a - 4 = -6
a = -6 + 4
a = -2
Therefore, the equation of the parabola in vertex form is:
y = -2(x + 3)^2 - 4