Question

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

Short answer

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

Step-by-step solution

Step 1. Write down the given information.

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

Step 2. Calculation.

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

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

Step 3. Conclusion.

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