Question

Which quadratic equation fits the data in the table?o y = −x − 4x + 1-O y = x2 – 4x − 1O y = x^ + 4x + 1O y = x − 4x + 1X0123456y1-2-3-21613

Answer 1

The easiest way to answer this question is to plug some numbers in for x and see if the output is consistent with the table. Right off the bat, we see that the y-intercept of the graph has to be positive 1 because the point (0,1) is given to us in the table. Because the second choice gives us an equation with a y-intercept of -1, we can cross that off.

Now, let's look at our second point (1, -2). We can try plugging 1 into each of the remaining three equations to see which one works. If we do this, we actually find that the only equation that corresponds to this point is the fourth equation:

`\begin{gathered} y=x^2-4x+1 \\ y=(1)^2-4(1)+1 \\ y=1-4+1 \\ y=-2 \end{gathered}`

Therefore, the correct equation is the following:

`y=x^2-4x+1`