Video: SAT Practice Test 1 • Section 3 • Question 17

A standard parabola in the 𝑥- and 𝑦-coordinate plane intersects the 𝑥-axis at (4, 0) and (−4, 0). What is the value of the 𝑥-coordinate of this parabola’s line of symmetry?

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Video Transcript

A standard parabola in the 𝑥- and 𝑦-coordinate plane intersects the 𝑥-axis at four, zero and negative four, zero. What is the value of the 𝑥-coordinate of this parabola’s line of symmetry?

So what I’ve done to help us answer this question is drawn a sketch. And this is a sketch of our parabola. A parabola is like this. So it’s either a u- or an n-shape. So I’ve now sketched on the n-shape. So what we know is what we have a parabola. And what we want to do is find the value of the 𝑥-coordinate of this parabola, where its line of symmetry is.

Well, from our sketch, it looks like our line of symmetry is gonna go directly down the 𝑦-axis. So it’s going to be where 𝑥 is equal to zero. So let’s test this and let’s work it out.

So what we want to do is find the midpoint between negative four and four, because the midpoint is going to be where the line of symmetry is going to be. To do that, we’re gonna add together four and negative four. And then we’re gonna divide it by two, because this will give us the midpoint of the line between negative four and four.

Well, when we work this out, the answer is going to be zero. And that’s because we have four. And then you add negative four. It’s the same as subtracting four from four, which is just zero. And zero divided by two is still zero.

So therefore, we can say that the 𝑥-coordinate of the parabola’s line of symmetry is going to be zero. And we’ve shown this through our sketch, but also through the calculation.

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