Question Video: Evaluating Quadratic Functions Mathematics

If 𝑓(𝑥) = −8𝑥² − 3𝑥 + 4, find 𝑓(−3).


Video Transcript

If 𝑓 of 𝑥 is negative eight 𝑥 squared minus three 𝑥 plus four, find 𝑓 of negative three.

We’ve been given a polynomial function. Remember, that’s a polynomial function where the powers of 𝑥 are all real positive integers. The highest power of 𝑥 in our polynomial function is two. So, we say that the degree or the order of the function is two. Now, the question wants us to find the value of 𝑓 of negative three. In other words, what’s the output of our function 𝑓 when its input is negative three? And so, to work this out, we’re going to replace or substitute 𝑥 with negative three throughout our function.

The first term in our function is negative eight 𝑥 squared. So, this becomes negative eight times negative three squared. Then, we subtract three times 𝑥. So, we’ll subtract three times negative three. The final term is four; that’s independent of 𝑥, so it’s still four. And of course, to evaluate this, we’re going to need to recall the order of operations. They tell us the order in which we’re performing the calculations. This is sometimes abbreviated as BIDMAS or PEMDAS. In either case, we evaluate the indices or the exponents before any multiplication. And so, we’re going to begin by evaluating negative three squared.

Well, negative three squared is negative three times negative three. A negative multiplied by another negative gives a positive. So, negative three squared is positive nine. And so, we have negative eight multiplied by nine minus three multiplied by negative three plus four. This time, we’re going to perform the multiplication before any addition or subtraction. Well, eight multiplied by nine is 72. And we know a negative multiplied by a positive is a negative.

We’re then going to subtract three multiplied by negative three. Well, three multiplied by negative three is negative nine. So, we’ll be subtracting negative nine. But of course, we know that subtracting a negative is the same as adding a positive. And so, we get negative 72 plus nine plus four. We now have addition and subtraction in the same calculation. Now, when this happens, we simply move from left to right. Negative 72 plus nine is negative 63.

When we add the nine, we move up the number line nine spaces. We’re going to add four to this, remembering once again that when we add four, we move up the number line four spaces. So, negative 63 plus four is negative 59. And so, given the quadratic function 𝑓 of 𝑥 is negative eight 𝑥 squared minus three 𝑥 plus four, we find 𝑓 of negative three to be equal to negative 59.

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