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How many points do you need to determine the equation of a parabola?

Answer 1

2: the vertex and another point

the vertex gives the values #(h,k)# another point gives #(x,y)# these can be plugged into vertex form, #y=a(x-h)^2 +k#

to get the equation of a parabola in standard form: once the four values are plugged into vertex form, the equation can be solved for the variable #a#

#b# can then be found using #x=((-b)/(2a))#

to find #c#, plug in the #a# and #b# values into #y=ax^2+bx+c# as well as the point from before (for #x# and #y#) and solve it

finally, plug the #a#, #b#, and #c# values into #y=ax^2+bx+c# and you have your equation in standard form

Though there may be other approaches, in general, two points are required.

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Answer 2

Julia Adams

You need three points to determine the equation of a parabola.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.