Question

How do you find the x and y intercepts for `y=2x^2-4x+3`?

Answer 1

y-intercept `=3`
There are no x-intercepts

Explanation:

Given `y=2x^2-4x+3`

The y-intercept is the value of `y` when `x=0`
`color(white)("XXX")y=2(0)^2-4(0)+3 = 3`

For a quadratic in the general form:
`color(white)("XXX")y=ax^2+bx+c`
the determinant `Delta = b^2-4ac` indicates the number of zeros.

`Delta {(< 0, rArr, "no solutions"),(=0, rArr, "one solution"),(>0,rArr,"two solutions"):}`

In this case
`color(white)("XXX")Delta = (-4)^2-4(2)(3) < 0`
so there are no solutions (i.e. no values for which the expression is equal to zero).

This can also be seen from a graph of this equation:
graph{2x^2-4x+3 [-6.66, 13.34, -0.64, 9.36]}

Answer 2

`(0, 3)`

Explanation:

`x = 0 \Rightarrow y = 0 - 0 + 3`

`y = 0 \Rightarrow x = frac{-b ± sqrt {b^2 - 4ac}}{2a}`

`a = 2, b = -4, c = 3`

But `Delta` < 0, then there is no real root `(x_0, 0)`.