### 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.