Suppose a parabola has a vertex (6, -6) and also passes through the point (8, -14). Write the equation of the parabola in vertex form
A. y=3(x-6)² - 6
B. y=-3(x+6)²-6
C. y= (x+6)²-6
D. y=-2(x-6)²-6
To write the equation of the parabola in vertex form, we can use the standard form of a parabola equation: y = a(x-h)² + k, where (h, k) is the vertex.
Given that the vertex is (6, -6), we have h = 6 and k = -6.
Now we need to find the value of "a". We can substitute the coordinates of the given point (8, -14) into the equation and solve for "a":
-14 = a(8-6)² - 6
-14 = 4a - 6
-14 + 6 = 4a
-8 = 4a
a = -8/4
a = -2
Therefore, the equation of the parabola in vertex form is:
y = -2(x-6)² - 6
So, the correct option is D. y = -2(x-6)² - 6.