Question

Can someone help me? I still don't understand this question.

Answer 1

$f(x) = -6x^2 + 7x + 4$

Step-by-step explanation:

For x = 1

$a(1)^2 + b(1) + c = 5 \Rightarrow a + b + c = 5$ (1)

For x = -3,

$a(-3)^2 + b(-3) + c = -71$

$\Rightarrow 9a - 3b + c = -71$ (2)

For x = 3,

$a(3)^2 + b(3) + c = -29$

$\Rightarrow 9a + 3b + c = -29$ (3)

Let's add Eqn(2) and Eqn(3) together to eliminate b:

$\Rightarrow 18a + 2c = -100$ (4)

Next, multiply Eqn(1) by 3 and then add to Eqn(2) to get

$\Rightarrow 12a + 4c = -56$ (5)

Then we want to eliminate c by multiplying Eqn(4) by -2 and then adding to Eqn(5) and we will get

$-24a = 144 \Rightarrow a = -6$

Now that we have the value for a, we can use either Eqn(4) or Eqn(5) to solve for c and we will get

$12(-6) + 4c = -56 \Rightarrow c = 4$

Using the values of a and c on Eqn(1), we find that $b = 7$ so therefore, our function f(x) has a form

$f(x) = -6x^2 + 7x + 4$