# How do you find the x and y intercepts for f(x)=2(x-5)^2 -50?

Jul 17, 2016

Intercepts on $x$-axis are $0$ and $10$; intercept on $y$-axis is $0$.

#### Explanation:

In the function $f \left(x\right) = 2 {\left(x - 5\right)}^{2} - 50$, $x$-intercept is given by $f \left(x\right) = 0$ and $y$-intercept is given by $f \left(0\right)$.

As such $x$-intercept is given by $2 {\left(x - 5\right)}^{2} - 50 = 0$ i.e. $2 \left({x}^{2} - 10 x + 25\right) - 50 = 0$ or

$2 {x}^{2} - 20 x = 0$ or $2 x \left(x - 10\right) = 0$ i.e. $x = 0$ and $x = 10$.

$y$-intercept is $f \left(0\right) = 2 {\left(0 - 5\right)}^{2} - 50 = 2 \cdot 25 - 50 = 0$.

Hence while intercepts on $x$-axis are $0$ and $10$; intercept on $y$-axis is $0$.