SOLUTION: Hello, I have to use 'completing the square' to put this equation into standard form, find the vertex, x- and y-intercepts. {{{2x^2+16x+9}}} I completed the square like this

Algebra ->  Equations -> SOLUTION: Hello, I have to use 'completing the square' to put this equation into standard form, find the vertex, x- and y-intercepts. {{{2x^2+16x+9}}} I completed the square like this      Log On


   



Question 367153: Hello, I have to use 'completing the square' to put this equation into standard form, find the vertex, x- and y-intercepts.
2x%5E2%2B16x%2B9
I completed the square like this:
2x%5E2%2B16x%2B9
x%5E2+%2B+8x+=+%28-9%2F2%29
x%5E2%2B8x%2B16=%2823%2F2%29
x%2B4=sqrt%2823%2F2%29
x=-4 +/- sqrt%2823%2F2%29
From here, I'm not sure how to put in standard form, but I know that once I have it in standard form, the vertex is (h,k).
Didn't I also find the x-intercept when I made the equation equal to zero to complete the square?
I plugged 0 in for x and solved for y to get y-intercept = 9.
If you could please show me how to finish completing the square to put in standard form, and also how I find the x-intercept I would greatly appreciate it! Thanks so much for your valuable time :)

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi,
Not sure exactly what the focus is here:
finding the vertex
The vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex
y = 2x%5E2%2B16x%2B9
y = 2[(x^2 + 8x + 9/2)]
y = 2[(x+4)^2 -16 + 9/2)]
y = 2(x+4)^2 + 2*(-23/2)
y = 2(x+4)^2 - 23
vertex (-4,-23)
graph%28+300%2C+300%2C-30%2C30%2C-30%2C30%2C2x%5E2+%2B16x+%2B9%29+