Question

Can someone solve this problem for me please? Find the quadratic polynomial whose graph goes through the points (-1,1), (0,2), and (1,7)?

Answer 1

A quadratic polynomial has the form \[y = ax^{2}+bx+c\]

Since you have 3 solution points, substitute each of them into the polynomial above:

For (0,2): \[2 = a(0)^{2} + b(0) + c = c\]
For (-1,1): \[1 = a(-1)^{2} + b(-1) + c = a - b + c = a - b + 2\]
For (1,7): \[7 = a(1)^{2} + b(1) + c = a + b + c = a + b + 2\]

Now you have two equations:
\[1 = a - b + 2\] and \[7 = a + b + 2\]

Simplify:
\[a - b = -1\] and \[a + b = 5\]

Solve the system of equations by substitution:
\[a = b - 1\]
\[a + b = (b - 1) + b = 2b - 1 = 5\]
\[b = 3\] and \[a = 2\]

Rewrite the quadratic polynomial with the constants:
\[y = 2x^{2} + 3x + 2\]

Answer 2

Thank you so much