The vertex of this parabola is at (3, -2). When the x-value is 4, the y-value is 3. What is the coefficient of the squared expression in the parabola's equation?

the equation of a parabola in its vertex form is y=a(x-h)²+k, where (h, k) is the vertex of the parabola.
in this case, h=3, k=-2, so y=a(x-3)-2
plug (4,3) in the equation: 3=a(4-3)²-2, a=5
so the coefficient of the squared expression is 5.