Question

What is the vertex form of `y= (x + 1)(x + 10)`?

Answer 1

`y = ( x + 11/2)^2 - 81/4`

Explanation:

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

Before we get to vertex form , require to distribute the brackets.

hence (x + 1 )(x + 10 ) `= x^2 + 11x + 10`

This is now in standard form and by comparison with `ax^2 + bx + c`

we obtain: a = 1 , b = 11 and c = 10

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

x-coord of vertex (h)`= (-b)/(2a) = -11/2`

and y-coord (k) = `(-11/2)^2 + 11(-11/2) + 10 = 121/4 - 121/2 + 10 = -81/4`
hence a = 1 and (h , k ) `= (-11/2 , -81/4 )`

`rArr y = (x + 11/2 )^2 - 81/4`