Question

Please help. . . . . . . .

Answer 1

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

4.
`y = (x + 2)^2`

Explanation:

In this problem, we are asked to find the equations in their factored form of the graphed parabolas.

3. We can see that the parabola's vertex is at (3, -4). We can plug the coordinates of that point into the vertex form equation:

`y=(x-a)^2 + b`

where
`(a,b)` is the vertex of the parabola.

`y=(x-3)^2 -4`

Then, we can expand the right side of the equation to an unfactored form.

`y=x^2-6x+9 -4`

`y=x^2-6x-5`

Finally, we can factor the right side of the equation.

`\boxed{y=(x-3)(x-2)}`

4. First, input the vertex's coordinates into the vertex form equation.

`y=(x - (-2))^2 + 0`

Then, simplify.

(Remember that subtracting a negative is the same as adding the positive)

`\boxed{y=(x+2)^2}`