How to find the function for a parabola with one x-intercept and one y-intercept, no data on symmetry or turning points

Question

The diagram given shows a positive shape and a turning point in the fourth quadrant.

x-intercept given (left) (-3/2;0) and y-intercept (0; -15/4)

Answer 1

y=4(x+1/2)^2 -4

vertex = (-1/2, -4) = minimum point= "turning point" where slope =0 where slope changes from - to +

upward opening parabola

2nd x intercept is (1/2, 0)

axis of symmetry: x=-1/2