Question

How do you write the equation given vertex (-7,4) and axis of symmetry x=-7 and measure of latus rectum 6, a<0?

Answer 1

Please see the explanation.

Explanation:

The axis of symmetry is a vertical line, therefore, this parabola is the type that opens up or down. The vertex equation of a parabola of this type is:

`y = a(x - h)^2 + k`

where `(h, k)` is the vertex.

Substitute -7 for h and 4 for k:

`y = a(x - -7)^2 + 4`

Let `L = "the length of the latus rectum" = 6`

One of the equations for "a" is:

`a = 1/(+-L)`

We are given that `a < 0`, therefore, we choose the negative value:

`a = 1/(-L)`

`a = -1/6`

Substitute -1/6 for "a" in the equation and you have the vertex form:

`y = -1/6(x - -7)^2 + 4`

For standard form, expand the square and combine like terms:

`y = -1/6x^2 - 7/3x -25/6`