Complete the table of values for
the function 𝑦 equals three 𝑥 squared minus two 𝑥.
In this question, we’re given a
function 𝑦 equals three 𝑥 squared minus two 𝑥 and five integer values of 𝑥 from
negative two to two. In order to complete the table, we
need to substitute each of these values in turn into the function. Let’s begin with positive two. When our 𝑥-value or input is equal
to two, then our 𝑦-value or output will be equal to three multiplied by two squared
minus two multiplied by two. Using our order of operations,
three multiplied by two squared is equal to 12. We need to square the two and then
multiply by three. Two multiplied by two is four. So we have 12 minus four. This is equal to eight. When 𝑥 is equal to two, 𝑦 is
equal to eight.
We can repeat this process when 𝑥
is equal to one. Three multiplied by one squared is
three, and two multiplied by one is two. As three minus two is equal to one,
when 𝑥 is equal to one, 𝑦 is equal to one.
When 𝑥 is equal to zero, 𝑦 is
equal to three multiplied by zero squared minus two multiplied by zero. Both parts of this calculation are
equal to zero. And zero minus zero is zero.
We now need to consider when 𝑥 is
negative, which is slightly more complicated. Squaring a negative number gives a
positive answer, as multiplying a negative by a negative is a positive. This means that three multiplied by
negative one squared is equal to three. Two multiplied by negative one is
negative two. But as we’re subtracting this,
we’re left with positive two. Three plus two is equal to
five. So when 𝑥 is equal to negative
one, 𝑦 is equal to five.
Three multiplied by negative two
squared is 12, as negative two squared is four. As two multiplied by negative two
is negative four, we need to add four to 12. Once again, we’re subtracting a
negative number. This gives us an output or 𝑦-value
of 16 when 𝑥 is negative two.
The five missing values in the
table are 16, five, zero, one, and eight. We could use these coordinate pairs
negative two, 16; negative one, five; and so on to graph the function 𝑦 equals
three 𝑥 squared minus two 𝑥. As our function is quadratic and
the coefficient of 𝑥 squared is positive, we will have a U-shaped parabola.