Question

What is the equation for the parabola graphed below

Answer 1

`y = x^2 - 2x -1`

Explanation:

General Form of a parabola :

`y = a (x - h)^2 + k`

Solving :

h and k refer to the point of the vertex. In this case, it's (1, -2), so :

`y = a(x - 1)^2 - 2`

Plug in values for x and y. In this case, they're (0, -1), so :

`-1 = a(0 - 1)^2 - 2\\-1 =a(1) - 2\\1 = a`

Plug in all values :

`y = ( x - 1)^2 -2`

Further simplifying :

`y = ( x - 1 )^2 - 2 \\y = (x^2-2x + 1) - 2\\y = x^2 - 2x -1`