Question

draw the graph of the polynomial f(x) = -x^2-2x+3​

Answer 1

Answer:

Your Graph is in the image shared below

Step-by-step explanation:

For making the graph,

we need to the following things

Graph will be a parabola as degree of polynomial is 2

Coefficient of x = -1 which is negative

so parabola will be opening downward

Now, to find the point on which parabola will cut x axis would be

zeroes or roots of $-x^2-2x+3=0$

$On factorizing\\-x^2-2x+3=0\\\\= x^2 +2x -3 =0\\= x^2 +(3-1)x -3 =0\\= x^2 +3x -x -3 =0\\= x(x+3) -1(x+3) =0\\=(x+3)(x-1)=0$

therefore, its zeroes or roots are -3 and 1

So parabola will cut x axis at (-3,0) and (1,0)

Now, to find the point where parabola will cut y axis would be

value of f(x) for x=0

therefore $f(x)= x^2-2x+3 = (0)^2-2(0)+3 = 3$

So, parabola will cut y axis at (0,3)

Now, we need to find the coordinates of vertex of parabola,

so, x coordinate = -b/2a= -(-2)/2(-1) = -1

now, for y coordinate, put x=-1 in  $f(x) =-x^2-2x+3$

= $-(-1)^2 -2(-1)+3 = -1 +2 +3 =4$

Therefore, vertex of parabola = (-1,4)

Now, You can use these information to make parabola.

If you need more precision, then

start putting different value of x in f(x). Like -

$x = 2, f(x)= -2^2-2(2)+3 = -4-4+3 = -5\\x=3, f(x) = -3^2-2(3)+3 = -9 -6 +3 = -12$

You can now also plot point (2,-5) and (3,-12)

Like this, you can plot as much points as you wish and plot the graph more precisely.

Hope You got the solution :-))

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