When we are given the vertex of the equation we can write the equation in the form :

y= a(x-h)²+k

Where (h,k) is the vertex.

If a is positive, the parabola opens upward (positive = smile). If a is negative, the parabola opens downward (negative = frown).

As the |a| gets bigger the parabola widens (value of x increases in relation to y).

Example : y = a(x + 3)² + 4

What is the vertex? : (-3,4) - Note the x value will always be the opposite of h (so if h is negative it will be positive. If it is positive it will be negative).

The reason for this is because we are looking to see what will make the inside of our parenthesis become 0. So if you have an x + 3 , the vertex will have a value of -3, which makes a(x + 3)^{2 equal to 0 which gives you the low or high point of the parabola (y) in k.}