Question

What is the equation of the quadratic function whose graph passes through (-3, 2), (-1, 0), and (1, 6)?

Answer 1

Answer:

f(x) = x² + 3x + 2

Step-by-step explanation:

Let the required f(x) be ax² + bx + c.

As the given points lie on the curve, they must satisfy the given equation. Therefore,

At (x, f(x)) = (-3, 2), x = -3 & f(x) = 2

=> a(-3)² + b(-3) + c = 2

=> 9a - 3b + c = 2 ...(1)

At (x, f(x)) = (-1, 0), x = -1 & f(x) = 0

=> a(-1)² + b(-1) + c = 0

=> a - b + c = 0

=> a = b - c ...(2)

At (x, f(x)) = (1, 6), x = 1 & f(x) = 6

=> a(1)² + b(1) + c = 6

=> a + b + c = 6 ...(3)

From (2) and (3):

=> (b - c) + b + c = 6

=> b = 3

In equation (1), 9a - 3b + c = 2

=> 9(b - c) - 3b + c = 2

=> 6b - 8c = 2

=> 6(3) - 2 = 8c

=> 2 = c

Therefore, a = b - c = 3 - 2 = 1

Hence, the required equation is:

= ax² + bx + c = (1)x² + (3)x + (2)

= x² + 3x + 2