[A table onscreen shows that: when x equals 0, y equals -3, when x equals 1, y equals -7, when x equals 2, y equals -19, when x equals 3, y equals -39. The narrator reads out the onscreen text.]

NARRATOR: Question two. Which equation possibly describes the relationship between x and y: y equals negative 4x minus 3, y equals 4x squared minus 3, y equals negative 4x squared minus 3, or y equals 4x minus 3? Looking at the table, we can see that as x increases by 1, y in the first instance decreases by 4, in the second instance decreases by 12 and in the third instance decreases by 20. Since as x changes by 1, y does not change by a constant amount, we can rule out any linear relationships. So that allows us to rule out the first and last equations, which are both linear.

Considering the relationship y equals 4x squared minus 3, if x equals 0, y would equal 4 multiplied by 0 squared minus 3, which is negative 3. So far so good. When x equals 1, y equals 4 multiplied by 1 squared minus 3, which equals 1, and doesn't fit the data. So we can rule out 4x squared minus 3.

This leaves one relationship. Let's check. If y is equal to negative 4x squared minus 3, when x equals 0, y will equal negative 4 multiplied by 0 squared minus 3, which gives negative 3. When x equals 1, y will equal negative 4 multiplied by 1 squared minus 3, which equals negative seven. When x equals 2, y will equal negative 4 multiplied by 2 squared minus 3, which equals negative 19. And when x equals 3, y will equal negative 4 multiplied by 3 squared minus 3, which equals negative 39. So therefore, y is equal to negative 4x squared minus 3 describes the relationship between x and y in the table given.