Question

draw the graph of y=xsquare-2x-3​

Answer 1

Given

We have given an equation y= x²-2x-3

To find

We have to find its coordinates and hence draw the graph

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Y= x²-2x-3

we see that x²-2x-3 is in the form of a quadratic equation so,we factorise it.

➙y= x²-2x-3

➙y= x²-3x-x-3

➙y= x(x-3)+1(x-3)

➙y= (x+1)(x-3)

Now, finding coordinates of y= (x+1)(x-3)

At x= -1

y = (-1+1)(-1-3)

y= 0

At x= 3

y= (3+1)(3-3)

y=0

At x= 0

y= (0+1)(0-3)

y= -3

At x= 1

y= (1+1)(1-3)

y= 2(-2)= -4

y= -4

Hence,the coordinates of x²-2x-3 are (-1,0),(3,0),(0,-3) & (1,-4).

Now,plot the coordinates into graph.

➙After plotting the coordinates we obtained a parabola graph.

Note : The graph of any quadratic polynomial or polynomial always be parabola

Answer 2

Given

We have given an equation y= x²-2x-3

To find

We have to find its coordinates and hence draw the graph

\sf\huge\bold{\underline{\underline{{Solution}}}}

Solution

Y= x²-2x-3

we see that x²-2x-3 is in the form of a quadratic equation so,we factorise it.

➙y= x²-2x-3

➙y= x²-3x-x-3

➙y= x(x-3)+1(x-3)

➙y= (x+1)(x-3)

Now, finding coordinates of y= (x+1)(x-3)

At x= -1

y = (-1+1)(-1-3)

y= 0

At x= 3

y= (3+1)(3-3)

y=0

At x= 0

y= (0+1)(0-3)

y= -3

At x= 1

y= (1+1)(1-3)

y= 2(-2)= -4

y= -4

Hence,the coordinates of x²-2x-3 are (-1,0),(3,0),(0,-3) & (1,-4).

Now,plot the coordinates into graph.

➙After plotting the coordinates we obtained a parabola graph.

Note : The graph of any quadratic polynomial or polynomial always be parabola