If you plot the directrix and the focus, you can see that the focus is to the left of the directrix. Since a parabola ALWAYS wraps itself around the focus, our parabola opens sideways, to the left to be specific. The formula for the parabola that opens to the left is

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

We will solve this for x at the end. The negative is out front because it opens to the left. If it opened to the right, it would be positive.

The vertex of a parabola is exactly halfway between the focus and the directrix, so our vertex coordinates h and k are (3, 6). P is defined as the distance between the vertex and the directrix, or the vertex and the focus. Since the vertex is directly between both the directrix and the focus, each distance is the same. P = 1. Filling in what we have now:

$-(y-6)^2=4(1)(x-3)$ which simplifies to

$-(y-6)^2=4(x-3)$

Now we will solve it for x.

$-(y-6)^2=4x-12$ and

$-(y-6)^2+12=4x$ so

$-\frac{1}{4}(y-6)^2+12=x$

4 0

3 years ago

Using the function f(x) = -3 x -5, calculate f(-7)

KonstantinChe [14]

Answer: X=16

Explanation: when you plug in -7 for x in the equation you have and just multiply it by -3 you will get 21 then subtract 5 and that will give yo 16

7 0

2 years ago

Write an algebraic expression to represent the phrase the different between two times b & 11

svet-max [94.6K]

are you sure you wrote that right?????

6 0

3 years ago