## Which quadratic equation fits the data in the table? A) y = x² − 7x − 1  B) y = −x² + 7x + 1  C) y = x² −7x + 1  D) y = x² + 7x + 1

Feb 2, 2018

Choice D works.

#### Explanation:

The table you have with $x$ and $y$ values should make the correct equation true. Remember the $x$ and $y$ values fit into each coordinate pair, or ordered pair, like this: $\left(x , y\right)$.
I looked first at the ordered pair $\left(0 , 1\right)$. If you put $0$ in for $x$ in equation A, you get $y = {0}^{2} - 7 \left(0\right) - 1 = 0 - 0 - 1 = - 1$. But in the ordered pair $\left(0 , 1\right)$, $x = 0$ and $y = 1$. When you plugged $0$ in for $x$, you got $y = - 1$, and that's not right.
Any of the others would give you $y = 1$ when you plug in $x = 0$.
Another easy point to look at is $\left(1 , 9\right)$. Out of the next three choices, we want to see if we get $y = 9$ when we plug $1$ in for $x$:

For B. we get: $- \left({1}^{2}\right) + 7 \left(1\right) + 1 = - 1 + 8 + 1 = 8$, and $8 \ne 9$.

Equation C: ${\left(1\right)}^{2} - 7 \left(1\right) + 1 = - 5$, and $- 5 \ne 9$.

Try D: ${\left(1\right)}^{2} + 7 \left(1\right) + 1 = 9$ and yes! $9 = 9$

So we don't need to try any other coordinate pairs; all of them should work, and these two don't work in equations A,B, or C.
I hope that helps!