Video Transcript
In the 𝑥𝑦-plane, the point three, eight lies on the graph of the function 𝑓. If 𝑓 of 𝑥 equals 𝑏 minus 𝑥 squared, where 𝑏 is a constant, what is the value of 𝑏?
So we’ve been given a point. That’s three, eight. And this is a point that lies on the graph of our function 𝑓. And 𝑓 of 𝑥 is equal to 𝑏 minus 𝑥 squared. So therefore, to find out what 𝑏 is going to be, we can substitute in our 𝑥 and 𝑦 values or 𝑥 and 𝑓 of 𝑥 values from our coordinate point three, eight, cause we can say that 𝑦 is equal to 𝑓 of 𝑥, like we just said. And then we’ve got our point three, eight. So our 𝑥 value is going to be three, and our 𝑦 value is going to be eight.
So if we substitute these values into our function, we’ll get eight is equal to 𝑏 minus three squared. So therefore, we’re gonna get eight is equal to 𝑏 minus nine. And that’s because three squared is nine, cause three multiplied by three is nine. So then to find out what 𝑏 is going to be, we add nine to each side of the equation. And when we do that, we get 17 is equal to 𝑏.
So therefore, we can say that if the point three, eight lies on the graph of function 𝑓 and 𝑓 of 𝑥 is equal to 𝑏 minus 𝑥 squared, where 𝑏 is a constant, the value of 𝑏 is going to be equal to 17.
