Y=2x^2+36x+170 setup equation this way to find the parabola.
Binomial should equal zero. Disregard the constant value of 170 and replace with c. So, 0=2x^2+36x+c is your equation. Switch your x from right to left side showing 2x^2+36x=0, divide by two and simplify. Setup like this: 2x^2/2 + 36x/2 = 0/2. Becomes, x2 +36x/2=0/2. Reduce common factors to equation reads x2+18x=0/2. Divide zero by two to get 0 so, it looks like this x^2+18x=0. Create a trinomial square on the left side of equation, you must find a value equal to the square of half of b, coefficient of x which is (b/2)^2=(9)^2 add this term to each side of the equation to get x^2+18x+(9)^2=0+(9)^2. Simplify. x^2+18x+81=81. Now, factor the perfect trinomial square into (x+9)^2 into (x+9)^2=81. Move the new constant to the left side equation. Becomes, 2(x+9)^2 - 162=0. Now, add the original constant to the new constant to get 2(x+9)^2 - 162+170=0. You must complete the square in the expression 2x^2+36x+170 for 2(x+9)^2 + 8. Now, reorder the right side of the equation, matching the vertex form of a parabola which is y=2(x+9)^2+8. You must use the vertex form y=a(x-h)^2+k to figure out the values of a, h, and k. a=2 h=-9 k=8 the vertex of (h, k) is (-9,8).
