Answer: (D) y = x² + 7x + 1
<u>Step-by-step explanation:</u>
Since a table of x,y-values are given, choose a coordinate and plug it into each equation to see which results in a true statement. If more than one equation is true, then choose another coordinate and plug it into the true equations from the previous coordinate.
Let's try (0, 1):
(A) y = x² - 7x - 1
1 = (0)² - 7(0) - 1
1 = -1
FALSE, So A is not the quadratic equation we are looking for
(B) y = x² - 7x + 1
1 = (0)² - 7(0) + 1
1 = 1
TRUE, So B could be the quadratic equation we are looking for
(C) y = -x² + 7x + 1
1 = -(0)² + 7(0) + 1
1 = 1
TRUE, So C could be the quadratic equation we are looking for
(D) y = x² + 7x + 1
1 = (0)² + 7(0) + 1
1 = 1
TRUE, So D could be the quadratic equation we are looking for
Let's try (1, 9) for B, C, and D:
(B) y = x² - 7x + 1
9 = (1)² - 7(1) + 1
9 = -5
FALSE, So B is not the quadratic equation we are looking for
(C) y = -x² + 7x + 1
9 = -(1)² + 7(1) + 1
9 = 7
FALSE, So C is not the quadratic equation we are looking for
(D) y = x² + 7x + 1
9 = (1)² + 7(1) + 1
9 = 9
TRUE, So D is the quadratic equation we are looking for!
