Question

1. Solve 2(x + 1)^2 = 18. What are the x-intercepts?

Answer 1

The x-intercepts are
`(2,0)` and
`(-4,0)`.

Explanation:

We are given the equation

`2(x+1)^2=18`

Begin by dividing both sides of the equation by 2:

`(x+1)^2=9`

Next, take the square root of both sides. Remember that there are two solutions to a square root, the positive and the negative root:

`x+1=\pm3`

Split the equation into two based on the two solutions:

`x+1=-3`

`x+1=3`

Solve each equation by subtracting 1 from both sides:

`x=-4\\ x=2`

Since the x-intercepts are the solutions to a quadratic, we know the solutions are (2,0) and (-4,0).