SOLUTION: Find the equation of a quadratic equation if the vertex is (-3, -2) and it passes through the point (-2, 0).

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Find the equation of a quadratic equation if the vertex is (-3, -2) and it passes through the point (-2, 0).      Log On


   

Question 254208: Find the equation of a quadratic equation if the vertex is (-3, -2) and it passes through the point (-2, 0).
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
vertex is (-3, -2) and it passes through the point (-2, 0)
All parabolas are symmetric, so the other point would be (-4,0).
We can create a quadratic model based on this using
Y+=+aX%5E2+%2B+bX+%2B+c
(i) -2+=+9a+%2B+-3b+%2B+c
(ii) 0+=+4a+-2b+%2B+c
(iii) 0+=+16a+-4b+%2B+c
eliminate the c from all 3 equations (i) -(ii) to get
(iv) -2+=+5a+-+b
and (iii) - (ii) to get
(v) 0+=+12a+-2b
multiply (iv) by -2 to get
(vi) 4+=+-10a+%2B+2b
add (v) and (vi) to get
(vii) 4+=+2a
* a = 2.
Sub -2 into a for (v) to get
* b = 12
Sub values of a and b into (i) to get
* c = 16
We get
y = 2x^2 + 12x + 16