Question

How do you find the x and y intercepts for `y=2x^2+8x+10`?

Answer 1

Set `y=0` and then `x=0` to find that there are no `x` intercepts and a single `y` intercept at `(0,10)`

Explanation:

The `x` and `y` intercepts of an equation are the points at which `y=0` and `x=0`, respectively. To find them, then, we just plug those values in and solve for the remaining variable.

`x` intercepts:

Setting `y=0`, we have

`2x^2+8x+10 = 0`

`=> x^2+4x+5 = 0`

Noting that the discriminant `4^2-4(1)(5) = -4` is less than `0`, this has no real solutions. Thus, there are no `x` intercepts.

`y` intercepts:

Setting `x=0`, we have

`y = 2*0^2+8*0+10`

`=> y = 10`

Thus there is a single `y` intercept at `(0,10)`.

If we look at the graph, it appears to agree with our findings:

graph{2x^2+8x+10 [-14.16, 14.32, -0.55, 13.69]}