What is the equation of a quadratic function whose graph passes through (-3,0) (4,0) and (1,24)?

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Answer 1 · 2018-05-15T12:29:05

The quadratic equation is # y = -2 x^2+2 x+24#

Let the quadratic equation be # y = ax^2+bx+c#

The graph passes through #(-3,0), (4,0) and (1,24)#

So these points will satisfy the quadratic equation.

#:. 0=9 a - 3 b +c; (1) , 0=16 a+ 4 b +c ;(2) # and

# 24= a+ b +c ; (3) # Subtracting equation (1) from equation

(2) we get, # 7 a +7 b = 0 :. 7(a+b)=0 # or

# a+b=0 :. a =-b# Putting #a=-b# in equation (3) we get,

#c=24#. Putting #a=-b , c=24# in equation (1) we get,

#0= -9 b -3 b +24 :. 12 b =24 or b =2 :. a =-2#

Hence the quadratic equation is # y = -2 x^2+2 x+24#

graph{-2x^2+2x+24 [-50.63, 50.6, -25.3, 25.32]} [Ans]