2x^2-4x+y+5=0

Question

We are currently graphing parabolas. This equation we are using completing the square to help make it into an equation where we are able to determine the vertex, focus, directrix, and axis of symmetry. After that, we must graph it including five points. I am at the step of the question where i am at (x-1)²+3/2= -y/2. I am not sure on how to continue to make it into y=a(x-h)²+k form. 

Answer 1

First, you should isolate all the x-terms from the y terms.

 

y = -2x² + 4x - 5

 

 

Now, we can put this in vertex form.  That is      y=a(x - h)²+k

 

y = -2(x² - 2x + 1) - 3

 

y = -2(x - 1)(x - 1) - 3

 

y = -2(x - 1)² - 3