What is the equation for the parabola graphed below

Question

asked Sep 22, 2023 165k views

1 Answer

Saltandwater · Answer 1 · 2023-09-27T17:12:43+0000

Answer:

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 :

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