Question

.find the vertex of the parabola whose equation is y = x2 2x 9. (-1, 8) (1, 12) (0, 9)

Answer 1

Option A is correct.

Explanation:

Given: Equation of Parabola, y = x² + 2x + 9

We have to find vertex of parabola.

We know that ( h , k ) is vertex of parabola in standard equation of parabola.

Standard equation of parabola, ( x - h )² = 4a (y - k )

First we rewrite the given equation into standard equation of parabola.

Consider,

y = x² + 2x + 9

using completing the square method, we get

Add 1² on both sides.

y + 1² = x² + 2x + 9 + 1²

y + 1 - 9 = x² + 2x + 1

y - 8 = ( x + 1 )²

( x + 1 )² = y - 8

Now, By comparing

we get, Vertex = ( -1 , 8 )

Therefore, Option A is correct.

Answer 2

y = x^2 + 2x + 9 = x^2 + 2x + 1 + 8 = (x + 1)^2 + 8
Vertex = (-1, 8)