Question

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?

Answer 1

y= (-.25) (x- (-2) )^2+4

Answer 2

a = 0.25

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.