To start to solve this problem, we need to know what vertex form is. The vertex form of a parabola is. The vertex form of a parabola is a(x-h) + k, where k is the vertical shift, h is the horizontal shift, and a is the value that tells the stretch.
To start to solve this equation, we want to start to create a difference of two squares.
y = 2(x²+x) We do this step to make the x² have a coefficient of 1
Now, we want to complete the square. To complete the square, we take 1/2 of the coefficient of x, and then square that.
1/2 * 1/2 = 1/4, and 1/4²=1/16
That means that we need to add 1/16 inside and outside the parenthesis.
We get:
y = 2(x²+1/2x + 1/16) - 1/16*2
We do -1/16*2 on the outside because since we added it inside the parenthesis, we need to take it away somewhere else (if that makes sense). The two is there because there is a two in front of the parenthesis.
We get:
y = 2(x+1/4)² - 1/8, by completing the square and simplifying, and this is the final answer.