Prove that the function given by the formula y = (2x-5) (3 + 8x) – (1-4x) ^ 2

Prove that the function given by the formula y = (2x-5) (3 + 8x) – (1-4x) ^ 2 is linear. Does the graph of this function belong to point A (-1; 10), point B (0; 16)?

In order to prove that the function y = (2x – 5) (3 + 8x) – (1 – 4x) ^ 2 is linear we will transform it.

So, open the brackets on the right side of the function and do the grouping and casting of similar ones.

y = 6x + 16x ^ 2 – 15 – 40x – (1 – 8x + 16x ^ 2) = 6x + 16x ^ 2 – 15 – 40x – 1 + 8x – 16x ^ 2 = 16x ^ 2 – 16x ^ 2 + 6x + 8x – 40x – 15 – 1 = -26x – 16.

y = -26x – 16 linear function.

Let’s check whether point A (-1; 10) and point B (0; 16) belong to the graph of this function.

A: 10 = -26 * (-1) – 16;

10 = 26 – 16;

10 = 10.

Belongs.

B: 16 = -26 * 0 – 16;

16 = -16.

not belong.