Answer:
y = 2[x + 2]^2 - 7
Step-by-step explanation:
We want to express y= 2x2 + 8x + 1 in vertex form.
Rewrite y= 2x2 + 8x + 1 as y= 2(x^2 + 4x) + 1
Now "complete the square" of x^2 + 4x:
Identify the coefficient of the x term. it is 4.
Take half of this: it is 2.
Square this result (that is, square 2) and then add the result to x^2 + 4x, and then subtract it: x^2 + 4x becomes x^2 + 4x + 4 - 4. Convince yourself that x^2 + 4x + 4 - 4 is identical to x^2 + 4x.
x^2 + 4x + 4 can be rewritten as (x + 2)^2.
Going back to our equation y= 2(x^2 + 4x) + 1 (see above),
replace "x^2 + 4x" in this equation with "(x + 2)^2 - 4:
Then: y= 2(x^2 + 4x) + 1 becomes:
y= 2( [x + 2]^2 - 4 ) + 1, or
y = 2[x + 2]^2 - 8 + 1, or y = 2[x + 2]^2 - 7
Compare this to the standard equation
y = a(x-h)^2 + k. We see that h = -2 and k = -7.
The given equation, expressed in vertex form, is y = 2[x + 2]^2 - 7. The vertex is at (-2, -7).
