Applied Mathematics

Question

Build a quadratic function that points down and has roots 2 and -4.

1. 1 mark for setting up the quadratic equation properly
2. 1 mark for showing appropriate work to find the equation
3. 1 mark for a quadratic function with roots 2 and -4
4. 1 mark for a quadratic function that points down

Answer 1

Let's break up the information given into math:

Roots at 2 and -4 mean that x = 2 and x = -4 when y = 0.

This can be converted into: x - 2 = 0 and x + 4 = 0

Multiplying both will still give us zero: (x-2)(x+4) = 0

Since the quadratic function is pointing down, we know that we have to add a negative sign:

y = -(x-2)(x+4) = - x² - 2x + 8

This in itself is the simplest quadratic function that has the roots and points down.

If you want this in "standard form" (y = a(x-h)² + k), complete the square:

y = -(x² + 2x) + 8

= -(x² + 2x + 1 - 1) + 8

y = -(x+1)² + 9