Answer the following:

Question

Find a quadratic equation f(x)=ax²+bx+c that passes through the points (0.6), (3, -6) and (-1, 14)

Answer 1

We have 3 unknoiwns, we need 3 equations:

Equation 1

6=a*0² + b*0 + c, 6=c

Equation 2

-6=a*3² + b*3 + c, -6=9a + 3b + c

Equation 3

14=a*(-6)² + b*(-6) + c, 14=36a - 6b + c

Since c=6 Use Equation2 2 and 3 to solve for a and b

-6=9a + 3b + 6 or -12=9a + 3b

14=36a - 6b +6 or 8=36a - 6b

Multiply Equation 2 by -4

-4*-12=-4*9a +-4*3b becomes 48=-36a - 12b

Add the modified Equation 2 to Equation 3

48=-36a - 12b

08=36a - 06b

56=0a -18b

56=-18b

b=56/-18 or -28/9

8=36a - 6*-28/9 or

8=36a + 56/3

-32/3=36a

-8/27=a

f(x)=-8x²/27 - 28x/9 + 6