Question

Can someone help?

What is the equation of the quadratic graph with a focus of (3, 1) and a directrix of y = 5?

Answer 1

The answers are
f(x) = one eighth (x − 3)2 + 3
f(x) = −one eighth (x − 3)2 + 3
f(x) = one eighth (x − 3)2 − 3
f(x) = −one eighth (x − 3)2 − 3

Answer 2

this question is really challenging

Answer 3

Do you know what a quadratic is to begin?

Answer 4

there are lots of methods that you can use to solve this, you may have been taught to use to distance formula...

or perhaps to find the focal length then the vertex...

Answer 5

the distance from any point on the graph to the focus = distance of the point from the directrix

distance from directrix = |y - 5|

distance from the focus = sqrt[ (x - 3)^2 + (y - 1)^2]

Answer 6

equate these 2 and simplify will give you your equation

Answer 7

Hint square both sides of the equation

Answer 8

aren't they already being squared?

Answer 9

you should always start by sketching the information so you know what you are looking at.



so looking at the information you may recognise the parabola is concave down since the focus is below the directrix

Answer 10

so a simple method is find the perpendicular distance between the focus and directrix