Video: Evaluating Quadratic Functions

Using the function 𝑦 = 𝑥² + 3, calculate the corresponding output for an input of 2.

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Video Transcript

Using the function 𝑦 equals 𝑥 squared plus three, calculate the corresponding output for an input of two.

Well, when we’re actually dealing with a function, our 𝑥 values are actually our inputs. So in this case, our 𝑥 value would be two. And our 𝑦 values and they are actual outputs. So what we’re trying to find is actually our 𝑦 value, so our output, if we put an input, so an 𝑥 value, of two into the function we’re given.

Another way of looking at this question is actually, as a function machine, we’ve got input. And then what we’re gonna do is I’ll square our 𝑥. Then we’re gonna add on three, and then we get our output. So in order to get our function, well, it says the input would be 𝑥. Then if we square it, we get 𝑥 squared. And then if we actually add three, we get 𝑥 squared add three. And that’s what we got with our original function.

So let’s think about this if we actually put the value of 𝑥 is two in. So we get an input of two. We then square it, which will give us four. And then we’d add three. Then once we’ve added three, we get an output of seven. So therefore, actually we’ve said that we’ve solved the problem because we’ve seen what happened if we put an input of two into a function 𝑦 equals 𝑥 squared plus three, because we found that the output is going to be seven. So we did that actually using a function machine.

Let’s actually see how we do it using the function and algebra. So if you got 𝑦 equals 𝑥 squared plus three, what we’re gonna do is substitute in 𝑥 equals two. And when we do that, we’re gonna get 𝑦 is equal to two squared, cause that’s our 𝑥 value, plus three. So this is gonna give us 𝑦 is equal to four plus three, cause two squared is four. So therefore, we get 𝑦 is equal to seven. So this gives us the same as we got using the function machine.

So we’ve worked out that the output is seven. So therefore, we can say that if we use the function 𝑦 equals 𝑥 squared plus three, then the corresponding output for an input of two is seven.

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