Question

Question #d9bde

Answer 1

`(0, 0) " " and " " (-5/2, 0)`

Explanation:

The `x` intercept of a function occurs when `y=0`, since every point on the `x` axis has a `y` coordinate of `0`.

Therefore, to find the `x` intercept(s), we need to plug in `color(red)0` for `color(blue)y` and solve for `x`:

`color(blue)y = 2x^2 + 5x - 3color(blue)y`

`color(red)0 = 2x^2 + 5x - 3(color(red)0)`

`0 = 2x^2 + 5x`

Notice that you can factor out `x` from both terms:

`0 = (x)(2x+5)`

Remember that if `a xx b = 0`, then either `a=0` or `b=0`.

`x = 0 " " or " " 2x+5 = 0`

`x = 0 " " or " " 2x = -5`

`x = 0 " " or " " x = -5/2`

So the `x` intercepts are:

`(0, 0) " " and " " (-5/2, 0)`

Final Answer