Question

using graph find zeroes
y=x²3x-4​

Answer 1

EXPLANATION.

There is two possibility in this question.

(1) = y = x² + 3x - 4.

(2) = y = x² - 3x - 4.

(1) = y = x² + 3x - 4.

From the first equation, we get.

Factorizes into middle term split, we get.

⇒ y = x² + 4x - x - 4.

⇒ y = x(x + 4) - 1( x + 4).

⇒ y = (x - 1)(x + 4).

⇒ (x - 1)(x + 4) = 0.

⇒ x = 1,x = -4.

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

⇒ y = (1)² + 3(1) - 4.

⇒ y = 1 + 3 - 4.

⇒ y = 4 - 4.

⇒ y = 0.

Their Co-ordinates = (1,0).

Put x = -4 in equation, we get.

⇒ y = (-4)² + 3(-4) - 4.

⇒ y = 16 - 12 - 4.

⇒ y = 16 - 16.

⇒ y = 0.

Their Co-ordinates = (-4,0).

Put x = 0 in equation, we get.

⇒ y = (0)² + 3(0) - 4.

⇒ y = 0 + 0 - 4.

⇒ y = -4.

Their Co-ordinates = (0,-4).

(2) = y = x² - 3x - 4.

From second equation, we get.

Factorizes into middle term split, we get.

⇒ y = x² - 4x + x - 4.

⇒ y = x(x - 4) + 1(x - 4).

⇒ y = (x + 1)(x - 4).

⇒ (x + 1)(x - 4) = 0.

⇒ x = -1,4.

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

⇒ y = (-1)² - 3(-1) - 4.

⇒ y = 1 + 3 - 4.

⇒ y = 4 - 4.

⇒ y = 0.

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

Put x = 4 in equation, we get.

⇒ y = (4)² - 3(4) - 4.

⇒ y = 16 - 12 - 4.

⇒ y = 16 - 16.

⇒ y = 0.

Their Co-ordinates = (4,0).

Put x = 0 in equation, we get.

⇒ y = (0)² - 3(0) - 4.

⇒ y = -4.

Their Co-ordinates = (0,-4).

Both the curves form upwards parabola.

(1) = Red curves indicates the equation,

⇒ y = x² + 3x - 4.

(2) = Blue curves indicates the equation,

⇒ y = x² - 3x - 4.

Answer 2

$\large\underline{\red{\sf \orange{\bigstar} Correct\; Question}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• using graph find zeroes y=x²3x-4 ?

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\green{\sf \red{\bigstar} Solution}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☯ (1) = y = x² + 3x - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

~ From the first equation, we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

~Factorizes into middle term split,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\red{\sf \orange{\bigstar} .}}$we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = x² + 4x - x - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = x(x + 4) - 1( x + 4).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = (x - 1)(x + 4).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ (x - 1)(x + 4) = 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ x = 1,x = -4.${\boxed{\blue{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large\underline{\pink{\sf \green{\bigstar} .}}$Put the value of x = 1 in equation, we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = (1)² + 3(1) - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 1 + 3 - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 4 - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 0.${\boxed{\green{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☢ Their Co-ordinates = (1,0)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Put x = -4 in equation, we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = (-4)² + 3(-4) - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 16 - 12 - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 16 - 16.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 0.${\boxed{\purple{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Their Co-ordinates = (-4,0).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Put x = 0 in equation, we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = (0)² + 3(0) - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 0 + 0 - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = -4.${\boxed{\green{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Their Co-ordinates = (0,-4).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

(2) = y = x² - 3x - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

~From second equation, we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

~Factorizes into middle term split,

we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = x² - 4x + x - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = x(x - 4) + 1(x - 4).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = (x + 1)(x - 4).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ (x + 1)(x - 4) = 0.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ x = -1,4.${\boxed{\orange{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = (-1)² - 3(-1) - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 1 + 3 - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 4 - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 0.${\boxed{\green{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Put x = 4 in equation, we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = (4)² - 3(4) - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 16 - 12 - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 16 - 16.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = 0.${\boxed{\red{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Their Co-ordinates = (4,0).

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

Put x = 0 in equation, we get.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = (0)² - 3(0) - 4.

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ::⇒ y = -4.${\boxed{\pink{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☯ Their Co-ordinates = (0,-4).${\boxed{\green{\checkmark{}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀