write the equation of a parabola in general form that has a
vertex of (5, 3) and a directrix of y = 1.

y = 1/8 x^2 - 5/4 x + 49/8.

Step-by-step explanation:

The vertex is always halfway between the directrix and the focus and the parabola always curves away from the directrix so the equation  will be of the form y = ax^2 + bx + c . It opens upwards. The absolute value of  p will be the distance from the vertex to the focus and the distance between the vertex and the focus. So

|p| = 3-1 = 2.  It is positive because the parabola opens upwards. The focus will be at  (5, 3+2) = (5, 5).

Using the formula:  

4p(y - k) = (x - h)^2    where  (h, k) is the vertex, we have:

8(y - 3) = (x - 5)^2

Converting this to general form:

8y - 24 = x^2 - 10x + 25

8y = x^2 - 10x + 49

y = 1/8 x^2 - 5/4 x + 49/8

i would say c is the best answer, hope it's right!

good luck! =)

cutie~

step-by-step explanation: