Answer:
y = (1/2)x² -2x
Step-by-step explanation:
recall that the general equation of a quadratic function is:
y = Ax² + Bx + C
given that 0 and 4 are roots, that means when x = 0 and x = 4, then y = 0
From this we can get 2 points on the curve, namely, (0,0) and (4,0)
substituting these points one at a time into the equation above,
for the first point (0,0),
0 = A (0)² + b(0) + C
C = 0
hence the equation becomes: y = Ax² + Bx
for the 2nd known point (4,0)
0 = A(4)² + B(4)
0 = 16A + 4B (divide both sides by 4)
0 = 4A + B
B = -4A ------------(eq 1)
we are given a 3rd point, vertex at (2,-2)
for (2,-2)
-2 = A(2²) + B(2)
-2 = 4A + 2B (divide both sides by 2)
-1 = 2A + B (subtract 2A from both sides)
B = -1 -2A --------(eq 2)
solving the system of equations using the method of your choice in eq1 and eq 2 gives:
A = 1/2 and B = -2
hence the equation is
y = (1/2)x² -2x
