SOLUTION: Find the equation of the parabola with vertex (-2,1) and x-intercepts -4 and 0. Thank you for your help.

Question 1002197: Find the equation of the parabola with vertex (-2,1) and x-intercepts -4 and 0.
Thank you for your help.
Found 2 solutions by MathLover1, josmiceli:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
given:
vertex (,) and
x-intercepts and
the vertex form of equation of the parabola:
if the vertex is at (,)=(,) we have

....now use x-intercepts to find
if x-intercepts , we have a point (,)=(,)

so, your equation is:

or, in standard form

Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If the x-intercepts are: and ,
Then you can say:

-------------------
You are given:
( -4,0 ) and ( 0,0 ) , so

-------------

If the equation has the form:

( )

------------
The formula for the x-coordinate of the vertex is:

( that confirms my answer )

Now I can say:

solving at ( -2,1 )

and since

and

---------------------
The equation is:

---------------------
check:
(0,0)

---------------------
(-4,0)

--------------
(-2,1)

OK

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