Question

What's the equation of the parabola that has its vertex at (8,–14) and a point (5,13) that lies on the curve?

Answer 1

Answer:

The expression with the described characteristics is: $y = 3*(x - 8)^2 - 14$. Therefore the correct answer is letter D.

Step-by-step explanation:

I believe there is a typo in the vertex's coordinate, I think it should be (8,14). I came to this conclusion by observing the possible answers, if the given vertex is correct then there are no correct answers among them. I made my best effort to explain the question in a way that can be generalized for different vertex's coordinates.

The equations are given in their vertex form. This form has the following structure:

$y = a*(x - h)^2 - k$

Where (h,k) are the vertex's coordinates, in our case (8, 14). This knowledge makes easier to determine a equation with the correct vertex as shown below:

$y = a*(x - 8)^2 - 14$

Where the value of "a" must be determined by applying the given point.

$13 = a*(5 - 8)^2 - 14\\13 = a*(3)^2 - 14\\a*9 = 27\\a = \frac{27}{9}\\a = 3$

The expression with the described characteristics is: $y = 3*(x - 8)^2 - 14$. Therefore the correct answer is letter D.