This table represents a quadratic function. x y 0 - 3 1 - 3.75 2 - 4 3 - 3.75 4 - 3 5 - 1.75 What is the value of a in the function's equation?

a = 0.25

Step-by-step explanation:

Our strategy to solve this problem will be to use the information given in the table to obtain first the value of c in the quadratic equation which has the form ax^2 + bx + c and then form a system of 2 linear equations and solve for the coefficients a and b as follow:

from x=0 and y=-3 a*0 + b * 0 + c = - 3

c = - 3

from x=1 and y = - 3.75

a * (1) + * (1) + (-3) = - 3.75

a + b = - 3.75 + 3 = - 0.75

from x = 2 and y = - 4

a * (2) ^2 + b * (2) + (-3) = - 4

4a + 2b = - 4 + 1

4a + 2b = - 1

Now we can solve the system f equations by elimination:

a + b = - 0.75

4a + 2b = - 1

multiply first equation by - 2 and add to the second and get

-2a - 2b = + 1.50

4a + 2b = - 1

2a = 0.50 and substituting into any of the equations get b = - 1

so the quadratic equation has a = 0.25 b = - 1 c = - 3

we can even plug the any of the other values for x given in the table and check the answer.