Question 999860
here's a good reference if you have the time and the inclination to look at it.
<a href = "http://www.purplemath.com/modules/parabola.htm" target = "_blank">http://www.purplemath.com/modules/parabola.htm</a>


the conics form of the equation is:


for vertical orientation:


4p(y-k) = (x-h)^2


for horizontal orientation:


4p(x-h) = (y-k)^2


vertical orientation means the parabola opens up or down.
horizontal orientation means the parabole opens to the left or to the right.


student is given that:


vertex is at the origin (0,0)
directrix is horizontal line through the point (0,-7)


the fact that the directrix is a horizontal line says that the parabole has vertical orientation.


the fact that the directrix is 7 units below the vertex says that the value of p is equal to 7.


that's because p is the distance from the directix to the vertex and also the distance from the focus to the vertex.


since the directrix is 7 units below the vertex, the focus is 7 units above the vertex.


the conics form of the equation is:


4p(y-k) = (x-h)^2


since (h,k) is the vertex and since the vertex is at (0,0), then h = 0 and k = 0.


the equation becomes:


4py = x^2


since p = 7, the equation becomes:


28y = x^2.


the parabola opens up or down (up is the coefficient if the (x-h)^2 term is positive and down if it is negative.


since the coefficient to the (x-h)^2 term is positive, the parabola opens up.


the graph of this parabola is shown below:


<img src = "http://theo.x10hosting.com/2015/102905.jpg" alt="$$$" </>


student said orientation was horizontal.
student said equation is 28x = y^2


the student got both the equation and the orientation wrong.


that would be selection D.