Question

Use the equation $x=3y^2+4y+1$ to find the y-intercept.

Short answer

The y-intercept of the equation $x=3y^2+4y+1$ is$\left(0,-\frac{1}{3}\right)\mathbf{and}\left(0,-1\right)$.

Step-by-step solution

Step 1. Write down the given information.

The given equation is $x=3y^2+4y+1$.

Step 2. Calculation.

The y-intercept of the equation $x=3y^2+4y+1$ can be obtained by plugging $x=0$ in $x=3y^2+4y+1$. Therefore,

$\begin{array}{c}x=3y^2+4y+1\left(\text{Given}\right)\\ \left(0\right)=3y^2+4y+\mathrm{1....}\left(\text{Plugging}x=0\right)\\ 3y^2+4y+1=0\\ \left(3y+1\right)\left(y+1\right)=0\\ 3y+1=0\text{or}y+1=0\\ y=-\frac{1}{3}\text{or}y=-1\end{array}$

Step 3. Conclusion.

The y-intercept of the equation $x=3y^2+4y+1$ is $\left(0,-\frac{1}{3}\right)\text{and}\left(0,-1\right)$.