Question

Draw the graphs of the given polynomial and fine the 0 . 3l justify the answers?​

Answer 1

EXPLANATION.

Draw Graph of the equation,

⇒ p(x) = x² - 6x + 9.

Factorizes the equation in middle term splits, we get.

⇒ y = x² - 6x + 9.

⇒ y = x² - 3x - 3x + 9.

⇒ y = x(x - 3) - 3(x - 3).

⇒ y = (x - 3)².

Zeroes of the equation, we get.

⇒ (x - 3)² = 0.

⇒ x = 3.

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

⇒ y = (3)² - 6(3) + 9.

⇒ y = 9 - 18 + 9.

⇒ y = 18 - 18.

⇒ y = 0.

Their Co-ordinates = (3,0).

Put x = 0 in equation, we get.

y = (0)² - 6(0) + 9.

y = + 9.

Their Co-ordinates = (0,9).

Equation = y = x² - 6x + 9.  makes curves upward parabola.

Answer 2

Given:

• P(x) = x² - 6x + 9

Factorise the given given equation,

→ y = x² - 6x + 9

→ y = x² - 3x - 3x + 9

→ y = x(x - 3) - 3(x - 3)

→ y = (x - 3)²

We get, The zeroes of the equation,

→ (x - 3)² = 0

→ x = 3

Now, put the value of x = 3 in equation.

→ y = (3)² - 6(3) + 9

→ y = 9 - 18 + 9

→ y = 18 - 18

→ y = 0

Hence:

• The coordinates are (3,0).

Now, put x = 0

→ y = (0)² - 6(0) + 9

→ y = +9

Hence:

• The coordinates are (0,9).

Therefore, Equation : y = x² - 6x + 9 forms curved upward parabola.