Question

Find the quation of the quadratic function with roots 0 and 4 and a vertex at (2,-2)

Answer 1

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