Question

How do you write the vertex form equation of the parabola `y=x^2+4x-5`?

Answer 1

`y = (x + 2 )^2 - 9`

Explanation:

The standard form of a quadratic function is `y = ax^2 + bx + c`

The function `y = x^2 + 4x - 5" is in this form "`

and by comparison a = 1 , b = 4 and c = -5

The vertex form of the equation is `y = a(x - h )^2 + k`

where (h , k ) are the coords of the vertex.

x-coord of vertex (h) `= (-b)/(2a) = (-4)/2 = -2`

and y-coord (k) = `(-2)^2 + 4 (-2) - 5 = 4-8-5 = -9`

hence (h , k ) = (-2 , -9) and a = 1

`rArr y = (x + 2 )^2 - 9 " is vertex form of equation "`