SOLUTION: Find the quadratic function that has given vertex and goes through the given point. (5,6), point (-1,0)

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Question 1125823: Find the quadratic function that has given vertex and goes through the given point. (5,6), point (-1,0)
Found 3 solutions by MathLover1, josgarithmetic, MathTherapy:
Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

Find the quadratic function that has given vertex and goes through the given point.
vertex: (,),
point: (,)

first, we recall a function , which will give us vertex (,)=(,)
So the function we are looking for should look like
,
and since the parabola passes through (,) , we have
, which means




and equation is:





Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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Find the quadratic function that has given vertex and goes through the given point. (5,6), point (-1,0)
----
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vertex (5,6)
through point (-1,0)

(Note that leading coefficient will be negative, and the other root is (11,0) , if choosing vertical symmetry axis).

, using the two zeros;
-
, plugging in vertex values;
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Find the quadratic function that has given vertex and goes through the given point. (5,6), point (-1,0)
Vertex form of a parabolic function: 

 -------- Substituting (- 1, 0) for [x, f(x)] and (5, 6) for (h, k)

This should give you an "a" value of , and the equation: 

That's IT!! 

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