Answer:
Step-by-step explanation:
If you're tasked to do this mathematically, you have to complete the square to get it into vertex, or work, form. Do that by first setting the equation equal to 0 then moving over the constant:
[tex]3x^2+2x=8[/tex] Next you have to have a +1 as the leading coefficient, and ours is a 3, so we factor it out:
[tex]3(x^2+\frac{2}{3}x)=8[/tex]. Now take half the linear term, square it, and add it in to both sides. Our linear term is 2/3. Half of 2/3 is 2/6 which reduces to 1/3. Squaring 1/3 gives us 1/9, so that's what we add in.
[tex]3(x^2+\frac{2}{3}x+\frac{1}{9})=8+\frac{1}{3}[/tex] to the right of the equals sign we added in 3*1/9 which is 3/9, which reduces to 1/3. Now we clean up both sides. The right side is easy; the left side, not so much. The reason we do this (complete the square) is to get a perfect square binomial on the left. When we re-write the left side into that perfect square binomial, we get
[tex]3(x+\frac{1}{3})^2=\frac{25}{3}[/tex] Now we move the constant back over and set the parabola back equal to y:
[tex]y=3(x+\frac{1}{3})^2-\frac{25}{3}[/tex] which shows us that the vertex is
[tex](-\frac{1}{3},-\frac{25}{3})[/tex]
