I have two problems that I need help with:
1) Find the vertex of the parabola y=x[squared]+10x+22.
2) Find the focus of the parabola y[squared]=12x.
1) The vertex of any parabola in the for y = ax^2 + bx + c occurs at x = -b/(2a), so in this case, it'll happen at x = -10/2 = -5, substituting x = -5 into the equation, y = -3.
So the vertex is at (-5 , -3)
2) The focus of the parabola y^2 = 12x. This is a parabola in the for y^2 = 4ax, so it's going to be a parabola facing left or right depending on what a is. Since y^2 = 4 * 3 * x in our situation, our parabola points right, and the focus is at (a,0) = (3,0).