Chapter 1.4, Problem 6QR

To determine

To find: The $x$ and $y$ intercepts of the equation $2y^2=x+1$ .

Answer to Problem 6QR

The $x$ intercepts is $-1$ , and $y$ -intercepts are $\frac{1}{\sqrt{2}}$ and $-\frac{1}{\sqrt{2}}$ .

Explanation of Solution

Given information: The equation is $2y^2=x+1$ .

Calculation:

Substitute 0 for $y$ in the given equation to find the $x$ intercepts.

  $\begin{array}{c}2{\left(0\right)}^2=x+1\\ x+1=0\\ x=-1\end{array}$

Substitute 0 for $x$ in the given equation to find the $y$ intercepts.

  $\begin{array}{c}2y^2=\left(0\right)+1\\ y^2=\frac{1}{2}\\ y=\pm \frac{1}{\sqrt{2}}\end{array}$

Therefore, the $x$ intercepts is $-1$ , and $y$ -intercepts are $\frac{1}{\sqrt{2}}$ and $-\frac{1}{\sqrt{2}}$ .