Question

2 Find an equation in the form y = ax? + bx + c for the parabola passing through the points. (3. – 56). (-1, - 16). (-2,- 51)

Answer 1

Answer:

Step-by-step explanation:

Many ways to do this in the details.

All start by writing three equations with three unknowns

-56 = a(3²) + b(3) + c

-56 = 9a + 3b + c          1)

-16 = a(-1²) + b(-1) + c

-16 = a - b + c               2)

-51  = a(-2²) + b(-2) + c  

-51  = 4a - 2b + c           3)

subtract equation 2 from equation 1

-40 = 8a + 4b

--10 = 2a + b

b = -10 - 2a                 4)

subtract equation 3 from equation 1

-5 = 5a + 5b

-1 = a + b                   5)

substitute 4 into 5

-1 = a + (-10 - 2a)

-1 = - a - 10

a = - 9

substitute a into 4

b = -10 - 2(-9)

b = 8

substitute a and b into any of 1, 2, or 3

-51  = 4(-9) - 2(8) + c

-51  = -36 - 16 + c

c = 1

y = -9x² + 8x + 1

We can use a plotting calculator to confirm our result.