### Video Transcript

At which value of π¦ does the graph of π¦ equals three π₯ squared plus two π₯ plus seven cross the π¦-axis?

To answer this question, we begin by recalling that we can use an equation to represent the π¦-axis. Itβs the vertical line with the equation π₯ equals zero. And so, to find the values of π¦ for which the graph of π¦ equals three π₯ squared plus two π₯ plus seven crosses the π¦-axis, weβre going to set each instance of π₯ equal to zero and solve for π¦.

By setting π₯ equal to zero, we get π¦ equals three times zero squared plus two times zero plus seven. Three times zero squared is zero. Two times zero is also zero. So, we have π¦ is equal to seven. And so, we find there is actually only one value of π¦ for which the graph of π¦ equals three π₯ squared plus two π₯ plus seven crosses the π¦-axis. Itβs seven.