Question Video: Completing Tables of Values for Functions Mathematics

Complete the table of values for the function 𝑦 = 3π‘₯Β² βˆ’ 2π‘₯.

03:19

Video Transcript

Complete the table of values for the function 𝑦 equals three π‘₯ squared minus two π‘₯.

In this question, we’re given a function 𝑦 equals three π‘₯ squared minus two π‘₯ and five integer values of π‘₯ 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 π‘₯-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 π‘₯ is equal to two, 𝑦 is equal to eight.

We can repeat this process when π‘₯ 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 π‘₯ is equal to one, 𝑦 is equal to one.

When π‘₯ 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 π‘₯ 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 π‘₯ 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 π‘₯ 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 π‘₯ squared minus two π‘₯. As our function is quadratic and the coefficient of π‘₯ squared is positive, we will have a U-shaped parabola.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.