Question

complete the table of values for y= x^2-2x-3

Answer 1

Answer:

x=3,y=0

x=-1,y=0

Step-by-step explanation:

We will have to factorise to get the value of x before solving for y

Let's solve

y=x^2-2x-3

To factorise x

x^2-3x+x-3

x(x-3)+1(x-3)

(x-3)+(x+1)

x-3=0

x=3

x+1=0

x=-1

Let's substitute the value of value to get the value for y

y=x^2-2x-3

When x is 3

y=3^2-2(3)-3

y=9-6-3

y=0

When x is-1

y=(-1)^2-2(-1)-3

y=1+2-3

y=0

Therefore when x is 3,y is 0

When x is -1,y is 0

Answer 2

For the values of 'x' that is -3, -2, -1, 0, 1, 2, 3, 4, 5 the values of 'y' is 12, 5, 0, -3, -4, -3, 0, 5, 12 respectively and this can be determined by factorising the given quadratic equation and then put the values of 'x' in it.

Given :

Quadratic equation - $y = x^2-2x-3$

To complete the table, first, factorize the given quadratic equation.

$y = x^2-2x-3$

$y = x^2-3x+x-3$

$y = (x-3)(x+1)$     ----- (1)

Now, according to the given table the values of 'x' is:

x = -3, -2, -1, 0, 1, 2, 3, 4, 5

Put the value of x=-3 in equation (1).

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

y = 12

Put the value of x=-2 in equation (1).

y = (-2-3)(-2+1)

y = 5

Put the value of x=-1 in equation (1).

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

y = 0

Put the value of x=0 in equation (1).

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

y = -3

Put the value of x=1 in equation (1).

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

y = -4

Put the value of x=2 in equation (1).

y = (2-3)(2+1)

y = -3

Put the value of x=3 in equation (1).

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

y = 0

Put the value of x=4 in equation (1).

y = (4-3)(4+1)

y = 5

Put the value of x=5 in equation (1).

y = (5-3)(5+1)

y = 12

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