Question Video: Determining Where the Graph of a Quadratic Equation Crosses the 𝑦-Axis

At which value of 𝑦 does the graph of 𝑦 = 3π‘₯Β² + 2π‘₯ + 7 cross the 𝑦-axis?

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Video Transcript

At which value of 𝑦 does the graph of 𝑦 equals three π‘₯ squared plus two π‘₯ 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 π‘₯ equals zero. And so, to find the values of 𝑦 for which the graph of 𝑦 equals three π‘₯ squared plus two π‘₯ plus seven crosses the 𝑦-axis, we’re going to set each instance of π‘₯ equal to zero and solve for 𝑦.

By setting π‘₯ 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 π‘₯ squared plus two π‘₯ plus seven crosses the 𝑦-axis. It’s seven.

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