What is the equation, in standard form, of a parabola that contains the following points (–2, 18), (0, 2), (4, 42)?

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Answer 1 · 2016-06-13T13:27:42

#y=3x^2-2x+2#

Standard form of equation of a parabola is #y=ax^2+bx+c#

As it passes through points #(-2,18)#, #(0,2)# and #(4,42)#, each of these points satisfies the equation of parabola and hence

#18=a*4+b*(-2)+c# or #4a-2b+c=18# ........(A)
#2=c# ........(B)
and #42=a*16+b*4+c# or #16a+4b+c=42# ........(C)

Now putting (B) in (A) and (C), we get\

#4a-2b=16# or #2a-b=8# and .........(1)

#16a+4b=40# or #4a+b=10# .........(2)

Adding (1) and (2), we get #6a=18# or #a=3#

and hence #b=2*3-8=-2#

Hence equation of parabola is

#y=3x^2-2x+2# and it appears as shown below

graph{3x^2-2x+2 [-10.21, 9.79, -1.28, 8.72]}