How do you make a quadratic model of (0,0)(14,4)(28,0)?

Question

y=ax^2+bx+c

Answer 1

The points are (0, 0), (14, 4) and (28,0)

The quadratic equation y  = ax ² + bx + c .

The above function passes through the points (0, 0), (14, 4) and (28,0)

If (x , y ) = (0, 0) then 0 =  a (0)² + b (0) + c  -------> 0 =  c -----> (1)

If (x , y ) = (14, 4) then 4 = a (14)² + b (14) + c -------> 4 = 196a +14b + c ----> (2)

If (x , y ) = (28, 0) then 0 = a (28)² + b (28) + c -------> 0 = 784a + 28b + c ----> (3)

Substitute the c  value in equations (2) & (3).

4 = 196a  + 14b  ---> (3)

0 = 784a  + 28b  ---> (4)

Solve (3) and (4) to eliminate b - variable and obtain two variable equation.

eq(4) - 2eq(3) ---->  0 - 8 = (784a + 28b ) - (392a + 28b )

392a  = - 8

a  = - 8/392

Substitute a = - 1/49 in equation (3)

4 = 196(-8/392) + 14b

4 = - 4 + 14b

8 = 14b

b  = 8/14 = 4/7

Substitute a  = -1/49 , b  = 4/7 , c  = 0 in quadratic equation.

y  = (-1/49)x ²+ (4/7)x

Required quadratic function is y  = - (1/49)x ² + (4/7)x

Graph

Choose values for x and find the corresponding values for y.

x	y = - (1/49)x ^2 + (4/7)x	(x, y )
5	y  = - (1/49)(5) ^2 + (4/7)5 = 2.34	(5,2.34)
25	y  = - (1/49)(25) ^2 + (4/7)25 = 1.53	(25, 1.53)

1.Draw a coordinate plane.

2.Plot the coordinate points.

3.Then sketch the graph, connecting the points with a smooth curve.