Question

What are the x– and y–intercepts of the quadratic equation `y = 2x^2 – 8x + 6`?

Answer 1

y-intercept: `(0,6)`
x-intercepts: `(1,0)` and `(3,0)`

Explanation:

1) To find the y-intercept, set `x=0` and solve for `y`:
`y = 2x^{2} - 8x + 6`
`y = 2(0)^{2} - 8(0) + 6`
`y = 0 - 0 + 6`
`y = 6`
y-intercept: `(0,6)`

2) To find the x-intercepts, set `y=0` and solve for `x`:
`y = 2x^{2} - 8x + 6`
`(0) = 2x^{2} - 8x + 6`
`0 = x^{2} - 4x + 3`
`0 = (x-1)(x-3)`
`0 = (x-1)` and `0 = (x-3)`
`1 = x` and `3 = x`
x-intercepts: `(1,0)` and `(3,0)`