SOLUTION: Find the equation of the quadratic function whose graph passes through the point (-1,3) and has vertex (2,-4) . ?

Question 725980: Find the equation of the quadratic function whose graph passes through the point (-1,3) and has vertex (2,-4) .
?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
If equation has the form ,
then the x co-ordinate of the vertex is at

given: vertex at (2,-4)

also:

(1)
-----------------------
Also given: (-1,3) is a solution

(2)
-----------------
Add (1) and (2)
(1)
(2)

and, since

--------------
also
(2)
(2)
(2)
(2)
The equation is:

--------------------------------
check: is the vertex at (2,-4) ?

OK
----------
Does it go through (-1,3) ?

OK

RELATED QUESTIONS
Find the rule of a quadratic function whose graph has the given vertex and passes through (answered by RAY100)

Find an equation of the parabola that has the indicated vertex and whose graph passes... (answered by Fombitz)

Find an equation of the parabola that has the indicated vertex and whose graph passes... (answered by MathLover1)

Find an equation of the parabola that has the indicated vertex and whose graph passes... (answered by FrankM)

Find the rule of a quadratic function whose graph has the given vertex and passes through (answered by rothauserc,josmiceli)

Find the quadratic function y=f(x) whose graph has a vertex (-2,3) and passes through the (answered by Solver92311)

For the following problem, find the quadratic function y=f(x) that has the given... (answered by math_tutor2020)

For the following problem, find the quadratic function y=f(x) that has the given... (answered by MathLover1)

find the quadratic function that has the indicated vertex and whose graph passes through... (answered by josgarithmetic)