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Answer:
y=-1x^2 -4x +5
Step-by-step explanation:
Given points (-2, 9), (-4, 5), and (1, 0)
General quadratic equation is y=ax^2 +bx+c
plug in each point and frame three equations
(-2,9)
equation 1
(-4,5)
5 = 16a -4b+c equation 2
(1,0)
0= a + b + c equation 3
Use equation 1 and 3
multiply third equation by -1 and then add it with equation 1
4a - 2a + c = 9
-a -b -c = 0
---------------------
3a - 3b = 9
divide whole equation by 3
a - b = 3 equation 4
use equation 2 and 3
16a -4b+c = 5
-a -b -c =0
------------------------
15a -5b = 5
divide whole equation by 5
3a -b= 1 equation 5
use equation 4 and 5 . multiply equation 5 by -1
-3a +b =-1
a - b = 3
-----------------------
-2a = 2
a= -1
plug it in equation 4 and find out b
a - b = 3
-1 - b = 3
add 1 on both sides
-b = 4 so b= -4
Now plug in the values and find out c
a + b+c = 0
-1 -4 + c= 0
-5 +c =0
c=5
Now plug in the values in the general equation
y=ax^2 +bx+c
y=-1x^2 -4x +5