# Where does the graph of  y = 3x^2 − 10x − 8 cross the x-axis?

May 28, 2018

$x = - \frac{2}{3} , x = 4$

#### Explanation:

$\text{to find where the graph crosses the x-axis set y = 0}$

$3 {x}^{2} - 10 x - 8 = 0$

$\text{using the a-c method to factor the quadratic}$

$\text{the factors of the product } 3 \times - 8 = - 24$

$\text{which sum to - 10 are - 12 and + 2}$

$\text{split the middle term using these factors}$

$3 {x}^{2} - 12 x + 2 x - 8 = 0 \leftarrow \textcolor{b l u e}{\text{factor by grouping}}$

$\textcolor{red}{3 x} \left(x - 4\right) \textcolor{red}{+ 2} \left(x - 4\right) = 0$

$\text{take out the "color(blue)"common factor } \left(x - 4\right)$

$\left(x - 4\right) \left(\textcolor{red}{3 x + 2}\right) = 0$

$\text{equate each factor to zero and solve for x}$

$x - 4 = 0 \Rightarrow x = 4$

$3 x + 2 = 0 \Rightarrow x = - \frac{2}{3}$
graph{3x^2-10x-8 [-10, 10, -5, 5]}