Question

A parabola has vertex (−2, −1) and passes through the point (1, 26). Find its equation.

Answer 1

`\text{Equation of parabola in vertex form,}\\\\~~~~~~~~~y = a(x-h)^2 +k\\\\\implies 26 = a(1+2)^2 -1~~~~~~~~;[(x,y) = (1,26)~ \text{and}~ (h,k) = (-2,-1)]\\\\\implies 26 = 9a -1\\\\\implies 9a = 26+1\\\\\implies 9a = 27\\\\\implies a = \frac{27} 9 \\\\\implies a = 3\\\\\text{Now,}\\\\~~~~~~~~y = 3(x+2)^2 -1~~~~~~~~~~;[\text{Vertex form.}]\\\\\implies y=3(x^2 +4x +4) -1\\\\\implies y = 3x^2 +12x +12 -1 \\\\\implies y=3x^2 +12x+11~~~~~~~~;[\text{Standard form.}]`