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

Dec 29, 2015

The x-intercepts occur where $f \left(x\right) = 0$ and the y intercept occurs when $x = 0$ giving $x = 1 - \frac{\sqrt{10}}{2}$ and $x = 1 + \frac{\sqrt{10}}{2}$ and $y = 3$

#### Explanation:

The x-intercepts occur where $f \left(x\right) = 0$ and the y intercept occurs when $x = 0$
$x = 0 \implies F \left(x\right) = - 2 \cdot 0 + 4 \cdot 0 + 3 = 3$
The y intercept is $y = 3$
Use the quadratic formula to find the x intercepts as this equation does not factor straightforwardly.
$x = \frac{- 4 \pm \sqrt{16 - 4 \left(- 2\right) \cdot 3}}{- 4}$
$x = 1 \pm \frac{\sqrt{40}}{- 4}$
$x = 1 - \frac{\sqrt{10}}{2}$ or $x = 1 + \frac{\sqrt{10}}{2}$