Question

given the equation 16(x - 1)=(y - 8)^2, determine whether the parabola opens up, down, left, or right. (1 point) down up right left

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola is \((y - k)^2 = 4p(x - h)\) (opens left or right) or \((x - h)^2=4p(y - k)\) (opens up or down).

Step2: Analyze the given equation

The given equation \(16(x - 1)=(y - 8)^2\) can be written as \((y - 8)^2 = 16(x - 1)\). Here, it is in the form \((y - k)^2 = 4p(x - h)\) where \(h = 1,k = 8\) and \(4p=16\) (so \(p = 4\)).

Step3: Determine the direction

Since the equation is of the form \((y - k)^2=4p(x - h)\) and \(p>0\) (because \(p = 4>0\)), the parabola opens to the right.

Answer:

right