Question

How do you find the intercepts for `y= x^2+4x-5`?

Answer 1

y-intercept
`y=-5`

x-intercepts
`x_1 =-5`
`x_2 =1`

Explanation:

an x-intercept is a point where `y=0`, and
a y-intercept is a point where `x=0`

x-intercepts: `0=x^2 + 4x -5`

`x^2 + 4x -5+ (4/2)^2=0+ (4/2)^2` complete the square
`(x + 2)^2 -5=4`
`(x + 2)^2 =9`
`x + 2=± 3`
`x =-2± 3`

`x_1 =-5`
`x_2 =1`

y-intercept: `y=(0)^2 + 4(0) -5=-5`

Check the graph

graph{x^2 + 4x - 5 [-9.96, 10.04, -8.72, 1.28]}