# How do you find the intercepts for f(x) = 2x^2 - 5x -3?

Jun 19, 2015

Given your function $y = f \left(x\right)$
y-inercept: $x = 0 , y = - 3$
x-intercept: ${x}_{1} = 3 , y = 0$
and ${x}_{2} = - \frac{1}{2} , y = 0$

#### Explanation:

First you set $x = 0$ into your equation and get $y = f \left(0\right) = - 3$.
Second you set $y = 0$ and solve the quadratic equation:
$2 {x}^{2} - 5 x - 3 = 0$ using the Quadratic Formula:
${x}_{1 , 2} = \frac{5 \pm \sqrt{25 + 24}}{4} = \frac{5 \pm 7}{4} =$
${x}_{1} = \frac{12}{4} = 3$
${x}_{2} = - \frac{2}{4} = - \frac{1}{2}$