The vertex form
y=a(x−h)2+k where (h,k) is the vertex.
Our question y=2x2+4x−30
We got different approaches for getting to the vertex form.
One is to use the formula for xcoordinate of the vertex and then using the value to find the y coordinate and write the given equation in the vertex form.
We are going to use a different approach. Let us use completing the square.
y=2x2+4x−30
We would first write the given equation in the following way.
y=(2x2+4x)−30 As you can see we have grouped the first and the second terms.
y=2(x2+2x)−30 Here 2 has been factored out from the grouped term.
Now take thex coefficient and divide it by 2. Square the result. This should be added and subtracted within the parenthesis.
y=2(x2+2x+(22)2−(22)2)−30
y=2(x2+2x+1−1)−30
y=2(x+1)2−1)−30 Note x2+2x+1=(x+1)(x+1)
y=2(x+1)2−2−30 Distributed the 2 and removed the parenthesis.
y=2(x+1)2−32 The vertex form.
