Question

draw the graphs of y=x2-x-6 and find zeros in each case

Answer 1

Please find the graph in the attached file

y=x^2-x-6

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

zeros are those values of x where the value of the function become zero.

So, x=3 & x=-2

Therefore, the zeros are 3 & -2

Answer 2

Zeros of the given function are x = -2, 3.

Step-by-step explanation:

Given:

The given function is.

$y = x^{2} -x-6$

Find the graph of given function in attached file.

The zero of a function is any replacement for the variable that will produce an answer of zero. Graphically, the real zero of a function is where the graph of the function crosses the x‐axis; that is, the real zero of a function is the x‐intercept(s) of the graph of the function.

$f(x)=x^{2} -x-6=0$

$x^{2} -x-6=0$

Notice that  $3\times 2 =6$

And that  3 - 2 = 1

$x^{2} -3x+2x-6=0$

$x(x-3)+2(x-3)=0$

$(x+2)(x-3)=0$

So, the zeros of the given function

$x+2=0\\x=-2$

$x-3=0\\x=3$

$x=-2,\ 3$

Therefore, the zeros of the function is -2, 3