Question

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

Answer 1

The x-intercepts occur where `f(x) = 0` and the y intercept occurs when `x = 0` giving `x = 1 -sqrt(10)/2` and `x = 1 + sqrt(10)/2` and `y=3`

Explanation:

The x-intercepts occur where `f(x) = 0` and the y intercept occurs when `x = 0`
`x = 0 => F(x) = -2*0 +4*0 +3 = 3`
The y intercept is `y=3`
Use the quadratic formula to find the x intercepts as this equation does not factor straightforwardly.
`x = (-4 +- sqrt(16 - 4(-2)*3))/(-4)`
`x = 1 +- sqrt(40)/(-4)`
`x = 1 -sqrt(10)/2` or `x = 1 + sqrt(10)/2`