Question

Type the correct answer in the box. Consider the table below. Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and care constants.X:-3,-2,-1,0,1Y:0.5,1,2.5,5,8.5complete the standard from equation representing the quadratic relationship displayed above, where A,B, and C are constants

Answer 1

The general form of a quadratic equation is given by:

y = ax² + bx + c

Use the given values on the table to obtain a system of equations.

for the point (-3 , 0.5):

0.5 = a(-3)² + b(-3) + c

0.5 = 9a - 3b + c (1)

for the point (-2 , 1):

1 = a(-2)² + b(-2) + c

1 = 4a - 2b + c (2)

for the point (0 , 5):

5 = a(0)² + b(0) + c

5 = c

replace c= 5 into the equation (1) and (2) and simplify like terms:

0.5 = 9a - 3b + 5

-4.5 = 9a - 3b (3)

1 = 4a - 2b + 5

-4 = 4a - 2b (4)

multiply the equation (3) by -2 and multiply the equation (4) by 3, then, sum the equations:

9 = -18a + 6b

-12 = 12a - 6b

-3 = -6a

from the previous equation, solve for a:

-3 = -6a

a = 1/2

Next, replace a=1/2 into the equation (4) and solve for b:

-4 = 4a - 2b

-4 = 4(1/2) - 2b

-4 = 2 - 2b

2b = 2 + 4

2b = 6

b = 3

Hence, the values of a, b and c are:

a = 1/2

b = 3

c = 5