Question

Draw the graph of y=x²-2x-3

Answer 1

EXPLANATION.

Draw the graph.

⇒ y = x² - 2x - 3.

As we know that,

Factorizes the equation into middle term splits, we get.

⇒ y = x² - 3x + x - 3.

⇒ y = x(x - 3) + 1(x - 3).

⇒ y = (x + 1)(x - 3).

Zeroes of the equation.

⇒ (x + 1)(x - 3) = 0.

⇒ x = - 1  and  x = 3.

Put the value of x = - 1 in the equation, we get.

⇒ y = x² - 2x - 3.

⇒ y = (-1)² - 2(-1) - 3.

⇒ y = 1 + 2 - 3.

⇒ y = 3 - 3.

⇒ y = 0.

Their Co-ordinates = (-1,0).

Putt the value of x = 3 in the equation, we get.

⇒ y = x² - 2x - 3.

⇒ y = (3)² - 2(3) - 3.

⇒ y = 9 - 6 - 3.

⇒ y = 9 - 9.

⇒ y = 0.

Their Co-ordinates = (3,0).

Put the value of x = 0 in the equation, we get.

⇒ y = x² - 2x - 3.

⇒ y = (0)² - 2(0) - 3.

⇒ y = - 3.

Their Co-ordinates = (0,-3).