Question

find the quadratic polynomial whose graph goes through the points (-2,5),(0,1),(2,13)

Answer 1

plot the points

so you know its concave up

the y intercept is 1

so its in the form

\[y = ax^2 + bx + 1\]

so substituting x = -2 y is 5

so

4a -2b + 1 = 5 Equation 1

and substituting x = 2

4a + 2b + 1 = 13 Equation 2

solve equations 1 and 2 simultaneously
by adding the equations to eliminate b

4a - 2b + 1 = 5
4a + 2b + 1 = 13
---------------
8a + 2 = 18

then a = 2

substitute a into equation 1 to find b

then you'll have your quadratic...