College Algebra

Question

Find the function y=ax^2 +bx + c whose graph contains the points (1,13),(-3,-47) and (3,7) Part 1 What is the​ Y function?

Answer 1

13 = a+b+c

7= 9a +3b+c

-47= 9a -3b +c

use substitution elimination or matrix algebra

54=6b

b=9

a+c=4

-20=9a +c

-20=9a+4-a= 8a+4

a= -3

c= 7

y= -3x^2 +9x +7 in standard form

y=ax^2+bx+c

or

y=-3(x-3/2)^2+55/4 in vertex form

y=a(x-h)^2+k

downward opening parabola, vertex=max=(1.5, 13.75)=(h,k)=(3/2,55/4)