# How do you find the zeros by rewriting the function y=2x^2-26x+24 in intercept form?

Jun 28, 2018

$x = 1 \text{ or } x = 12$

#### Explanation:

$\text{the intercept form is } y = a \left(x - p\right) \left(x - q\right)$

$\text{where p and q are the x-intercepts}$

$\text{to obtain this form factor the quadratic}$

$\text{to obtain the zeros set y = 0}$

$2 {x}^{2} - 26 x + 24 = 0$

$\text{divide all terms by 2}$

${x}^{2} - 13 x + 12 = 0$

$\text{the factors of "+12" which sum to "-13}$

$\text{are "-1" and } - 12$

$\left(x - 1\right) \left(x - 12\right) = 0 \leftarrow \textcolor{b l u e}{\text{in intercept form}}$

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

$x - 1 = 0 \Rightarrow x = 1$

$x - 12 = 0 \Rightarrow x = 12$