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

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Answer 1 · 2018-04-21T01:30:51

#y=11/4x^2-3/2x+4#

The standard form of a quadratic equation is

#y=ax^2+bx+c#.

Here, when #x=0#, #y=4#, so it is easy to determine #c#.

#4=a*0^2+b*0+c=c#

#c=4#

We have two more points with which to create two equations and two unknowns, #a#, and #b#.

#18=a(-2)^2+b(-2)+4=4a-2b+4#

#42=a(4)^2+b(4)+4=16a+4b+4#

We can subtract 4 from both sides of these equations and divide the second equation by 2.

#4a-2b=14#

#8a+2b=19#

Now add the two equations together.

#12a=33#

#a=11/4#

Substitute this value of #a# into either equation to get

#b=-3/2#

This makes our final equation

#y=11/4x^2-3/2x+4#