# Question #d9bde

Jul 19, 2017

$\left(0 , 0\right) \text{ " and " } \left(- \frac{5}{2} , 0\right)$

#### Explanation:

The $x$ intercept of a function occurs when $y = 0$, since every point on the $x$ axis has a $y$ coordinate of $0$.

Therefore, to find the $x$ intercept(s), we need to plug in $\textcolor{red}{0}$ for $\textcolor{b l u e}{y}$ and solve for $x$:

$\textcolor{b l u e}{y} = 2 {x}^{2} + 5 x - 3 \textcolor{b l u e}{y}$

$\textcolor{red}{0} = 2 {x}^{2} + 5 x - 3 \left(\textcolor{red}{0}\right)$

$0 = 2 {x}^{2} + 5 x$

Notice that you can factor out $x$ from both terms:

$0 = \left(x\right) \left(2 x + 5\right)$

Remember that if $a \times b = 0$, then either $a = 0$ or $b = 0$.

$x = 0 \text{ " or " } 2 x + 5 = 0$

$x = 0 \text{ " or " } 2 x = - 5$

$x = 0 \text{ " or " } x = - \frac{5}{2}$

So the $x$ intercepts are:

$\left(0 , 0\right) \text{ " and " } \left(- \frac{5}{2} , 0\right)$