SOLUTION: Complete the general form equation of the parabola that passes through (2,−21)with vertex at (−1,−3) Enter the quadratic expression in general form, ax^2+b

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Complete the general form equation of the parabola that passes through (2,−21)with vertex at (−1,−3) Enter the quadratic expression in general form, ax^2+b      Log On


   

Question 1126203: Complete the general form equation of the parabola that passes through
(2,−21)with vertex at (−1,−3)
Enter the quadratic expression in general form,
ax^2+bx+c.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
y=a%28x-%28-1%29%29%5E2-3
y=a%28x%2B1%29%5E2-3
y%2B3=a%28x%2B1%29%5E2
a=%28y%2B3%29%2F%28x%2B1%29%5E2
-
a=%28-21%2B3%29%2F%282%2B1%29%5E2
a=-18%2F9
a=-2
-
y=-2%28x%2B1%29%5E2-3, which you can 'simplify' .

y=-2%28x%5E2%2B2x%2B1%29-3
-2x%5E2-4x-2-3
-2x%5E2-4x-5, here in ax^2+bx+c form.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Complete the general form equation of the parabola that passes through
(2,−21)with vertex at (−1,−3)
Enter the quadratic expression in general form,
ax^2+bx+c.
Vertex from: matrix%281%2C3%2C+y%2C+%22=%22%2C+a%28x+-+h%29%5E2+%2B+k%29

matrix%281%2C3%2C+-+21%2C+%22=%22%2C+a%282+-+-+1%29%5E2+-+3%29 ------- Substituting (2, - 21) for (x, y) and (- 1, - 3) for (h, k) 

- 21 = 9a - 3

- 21 + 3 = 9a

- 18 = 9a

matrix%281%2C5%2C+a%2C+%22=%22%2C+%28-+18%29%2F9%2C+%22=%22%2C+-+2%29

matrix%281%2C3%2C+y%2C+%22=%22%2C+-+2%28x+%2B+1%29%5E2+-+3%29 ------- Substituting - 2 for a, and (- 1, - 3) for (h, k) 

matrix%281%2C3%2C+y%2C+%22=%22%2C+-+2%28x%5E2+%2B+2x+%2B+1%29+-+3%29