How do you write the quadratic function in standard form given points #(-4,-7)#, #(-3,3)#, #(3, -21)#?

1 Answer
mizoo
Apr 28, 2018

#y = -2x^2 -4x + 9#

Explanation:

#y = ax^2 + bx + c#

#(-4, -7):#
# -7= a(-4)^2 + b(-4) + c#
#16a - 4b + c = -7 => eq_1#

#(-3,3):#
#3 = a(-3)^2 + b(-3) + c#
#9a - 3b + c = 3 => eq_2#

#(3,-21):#
#-21 = a(3)^2 + b(3) + c#
#9a + 3b + c = -21 => eq_3#

#eq_(1,2&3)#
#16a - 4b + c = -7#
#9a - 3b + c = 3#
#9a + 3b + c = -21#
#=> a = -2, b = -4, c = 9#

#y = -2xxx^2 + -4xxx +9#
#y = -2x^2 -4x + 9#

https://www.desmos.com/calculator/njo2ytq9bp

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