# What are the x and y intercepts for y = 1/2 (x-4)^2 +18?

Mar 6, 2018

There is no $x$-intercept. $y$-intercept is $26$.

#### Explanation:

To find $x$-intercept of any curve, just put $y = 0$

and to $x$-intercept of any curve, just put $x = 0$.

Hence $x$-intercept of $y = \frac{1}{2} {\left(x - 4\right)}^{2} + 18$ is given by $\frac{1}{2} {\left(x - 4\right)}^{2} + 18 = 0$ or $\frac{1}{2} {\left(x - 4\right)}^{2} = - 18$. But this is not possible asLHS cannot be negative. Hence, we do not have $x$-intercept.

For $y$-intercept of $y = \frac{1}{2} {\left(x - 4\right)}^{2} + 18$, put $x = 0$ and then $y = \frac{1}{2} \cdot {\left(- 4\right)}^{2} + 18 = 26$. Hence $y$-intercept is $26$.

graph{y=1/2(x-4)^2+18 [-77, 83, -18.56, 61.44]}