Questions on Algebra: Quadratic Equation answered by real tutors!

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> Questions on Algebra: Quadratic Equation answered by real tutors!     (Log On)
Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebra Solved!™: algebra software that solves YOUR algebra homework problems with step-by-step help!

   

Question 151404: How would I go about writing the quadratic function, in (standard) form, which has a vertex of (-6, 2) and passes through (5, 12)?
The standard form is y= a(x-h)^2+k , so i would put -6 as h and 2 as k but from there I am stuck.: How would I go about writing the quadratic function, in (standard) form, which has a vertex of (-6, 2) and passes through (5, 12)?
The standard form is y= a(x-h)^2+k , so i would put -6 as h and 2 as k but from there I am stuck.
Answer by jim_thompson5910(9421) About Me  (Show Source):
You can put this solution on YOUR website!
y= a(x-h)^2+k Start with the given equation.


y= a(x-(-6))^2+2 Plug in h=-6 and k=2


y= a(x+6)^2+2 Rewrite x-(-6) as x+6


Since the quadratic passes through (5, 12), this means that if you plug in x=5, you will get y=12. So we can plug in x=5 and y=12 to solve for "a"

12= a(5+6)^2+2 Plug in x=5 and y=12


12= a(11)^2+2 Add


12= a(121)+2 Square 11 to get 121


12= 121a+2 Rearrange the terms


10= 121a Subtract 2 from both sides.


10/121= a Divide both sides by 121.


So the value of "a" is a=10/121



This means that the equation is


y= (10/121)(x+6)^2+2