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Video: Finding the Set of Zeros of a Quadratic Function

Bethani Gasparine

What are the zeros of the function 𝑓(𝑥) = 2(𝑥 − 1)² − 7?

00:45

Video Transcript

What are the zeros of the function 𝑓 of 𝑥 equals two times 𝑥 minus one squared minus seven.

If we’re finding the zeros of this function, we need to set it equal to zero and solve. So the first thing we should do is add seven to both sides. And now we can divide both sides by two. So 𝑥 minus one squared is equal to seven-halves and now we can square root both sides which is equal to 𝑥 minus one equals plus or minus the square root of seven-halves. And now we add one to the other side of the equation to the right. So we have one plus or minus the square root of seven-halves.

Separating now, we could say 𝑥 equals one plus square root of seven-halves and 𝑥 equals one minus square root of seven-halves.