Question

What is the equation of the quadratic graph with a focus of (-4, 17/8) and a directrix of y = 15/8?

a) f(x) = -2x^2 + 16x - 24
b) f(x) = -2x^2 + 15x - 2
c) f(x) = 2x^2 + 12x - 10
d) f(x) = 2x^2 + 16x + 34

Answer 1

The equation of the quadratic graph with a focus of (-4, 17/8) and a directrix of y = 15/8 is f(x) = (1/9)(x^2 + 8x + 35) - 1.

Step-by-step explanation:

The equation of the quadratic graph with a focus of (-4, 17/8) and a directrix of y = 15/8 can be found using the formula for a parabola with a vertical axis:

For a parabola with a vertical axis, the equation is of the form (x - h)^2 = 4p(y - k), where (h, k) is the vertex and p is the distance between the vertex and the focus or directrix.

In this case, the vertex is at (h, k) = (-4, 1) and the distance between the vertex and the focus or directrix is p = 17/8 - 1 = 9/8.

Substituting these values into the equation, we get:

x^2 + 8x + 35 = 9(y + 1)

So the equation of the quadratic graph is f(x) = (1/9)(x^2 + 8x + 35) - 1.