Precalculus, Chapter 1, 1.2, Section 1.2, Problem 28

Determine the intercepts and graph equation $4x^2 + y = 4$ by plotting points. Be sure to label the intercepts.

$x$-intercept:


$
\begin{equation}
\begin{aligned}

4x^2 + y =& 4
&& \text{Given equation}
\\
4x^2 + 0 =& 4
&& \text{To find the $x$-intercept, we let } y = 0
\\
4x^2 =& 4
&&
\\
x^2 =& 1
&&
\\
x =& \pm 1
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(1,0)$ and $(-1,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

4x^2 + y =& 4
&& \text{Given equation}
\\
4(0)^2 + y =& 4
&& \text{To find the $y$-intercept, we let } x = 0
\\
y =& 4
&&

\end{aligned}
\end{equation}
$


The $y$-intercept is $(0,4)$