At which value of 𝑦 does the graph of 𝑦 equals three 𝑥 squared plus two 𝑥 plus seven cross the 𝑦-axis?
To answer this question, we begin by recalling that we can use an equation to represent the 𝑦-axis. It’s the vertical line with the equation 𝑥 equals zero. And so, to find the values of 𝑦 for which the graph of 𝑦 equals three 𝑥 squared plus two 𝑥 plus seven crosses the 𝑦-axis, we’re going to set each instance of 𝑥 equal to zero and solve for 𝑦.
By setting 𝑥 equal to zero, we get 𝑦 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 𝑦 is equal to seven. And so, we find there is actually only one value of 𝑦 for which the graph of 𝑦 equals three 𝑥 squared plus two 𝑥 plus seven crosses the 𝑦-axis. It’s seven.