Point (-6,-2) lies on a parabola that has its vertex at (0,1). Write the equation of the parabola. Indicate whether the graph opens up or down.
To write the equation of a parabola, you need to know its vertex form, which is given by the equation:
y = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola and a determines whether the graph opens up or down.
In this case, the vertex of the parabola is given as (0, 1).
We also know that the point (-6, -2) lies on the parabola. Therefore, we can substitute the coordinates of this point into the equation and solve for the value of a.
Substituting (-6, -2) into the equation, we have:
-2 = a(-6 - 0)^2 + 1
Simplifying this equation, we get:
-2 = 36a + 1
Subtracting 1 from both sides:
-3 = 36a
Dividing both sides by 36:
a = -3/36
Simplifying this equation further, we get:
a = -1/12
Now, we have the value of a. Therefore, the equation of the parabola is:
y = (-1/12)(x - 0)^2 + 1
Simplifying this equation:
y = (-1/12)x^2 + 1
Now, we can determine whether the graph opens up or down.
Since the coefficient of x^2 is negative (-1/12), the parabola opens downward.
Therefore, the equation of the parabola is y = (-1/12)x^2 + 1, and its graph opens down.