Question

Find the x-intercepts of the parabola with vertex (3,-2) and y intercept at (0,7) write your answer in this form (x1,y1)(x2,y2)

Answer 1

Greetings!

As you already have the vertex, the equation for this is:

`y = A(x - b)^(2) + k`

Where (b, k) is the vertex.

So by plugging all this in using the vertex coordinates you get:

`y = 3(x - 3)^(2) - 2`

To find the x intercepts, you set the y value to 0, so:

`0 = 3(x - 3)^(2) - 2`

Now you can move the negative two over, making it a positive two:

`2= 3(x - 3)^(2)`

Now, if you divide everything by three you get:

`(2)/(3) = (x - 3)^(2)`

Then you can simple square root both sides to get x - 3 by itself:

`\sqrt{(2)/(3)} = x-3`

Then finally move the negative three over to the other side so that x is by itself:

3 ±
`\sqrt{(2)/(3)} = x`

Which means that the two x intercepts are:

(
`3 + \sqrt{(2)/(3)}`,0) and (
`3 - \sqrt{(2)/(3)}`,0)

Hope this helps!