ASK A QUESTION Find the quadratic function y=ax^2 +bx+c whose graph passes through the given points.

Question

(1,-1) (3,23) (-1,7)

Answer 1

y=ax^2+bx+c

replace x and y by each pair of points and set up three equations in 3 unknowns

-1=a+b+c

23=9a+3b+c

7=a-b+c

subtract equation 1 from equation 3

8=-2b

b=-4

replace b by -4 in equations 1 and 2

-1=a-4+c

23=9a-12+c

simplify

3=a+c

35=9a+c

subtract the first equation from the second one

32=8a

a=4

replace a by 4 and b by -4 in equation 3

7=4+4+c

7-8=c

c=-1

a=4, b=-4, c=-1

y=4x^2-4x-1 is the quadratic function