Draw the graph of polynomial f(x)=3-2x-x2
Answers
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Let y = f(x) or, y = 3 - 2x - x2. Let us list a few values of y = 3 - 2x - x2 corresponding to a few values of x as follows : x -5 -4 -3 -2 -1 0 1 2 3 4 y=3-2x-x2 -12 -5 0 3 4 3 0 -5 -12 -21 Thus, the following points lie on the graph of the polynomial y = 2 - 2x - x2: (-5, -12), (-4, -5), (-3, 0), (-2, 4), (-1, 4), (0, 3), (1, 0), (2, - 5), (3, -12) and (4, - 21). Let plot these points on a graph paper and draw a smooth free hand curve passing through these points to obtain the graphs of y = 3 - 2x - x2. The curve thus obtained represents a parabola, as shown in figure. The highest point P(-1, 4), is called a maximum points, is the vertex of the parabola. Vertical line through P is the axis of the parabola. Clearly, parabola is symmetric about the axis. Observations : Following observations from
the graph of the polynomial f(x) = 3 - 2x - x2 is as follows : (i) The coefficient of x2 in f(x) = 3 - 2x - x2 is - 1 i.e. a negative real number and so the parabola opens downwards. (ii) D =b2 - 4ax = 4 + 12 = 16 > 0. So, the parabola cuts x-axis two distinct points. (iii) On comparing the polynomial 3 - 2x - x2 with ax2 + bc + c, we have a = - 1, b = - 2 and c = 3. The vertex of the parabola is at the point (-1, 4) i.e. at (-b/2a,-D/4a), where D = b2 - 4ac. (iv) The polynomial f(x) = 3 - 2x - x2 = (1 - x) (x + 3) is factorizable into two distinct linear factors (1 - x) and (x + 3). So, the parabola cuts X-axis at two distinct points (1, 0) and (-3, 0). The co-ordinates of these points are zeros of f(x).Read more on Sarthaks.com - https://www.sarthaks.com/249798/draw-the-graphs-of-the-quadratic-polynomial-f-x-3-2x-x-2
Brainiest answer please.
Refer the graph attached.
Step-by-step explanation:
Given : Polynomial
To find : Draw the graph of polynomial ?
Solution :
To plot the graph of the polynomial we have to find different points of x and f(x).
Since it is quadratic the curve form in parabolic form.
x f(x)
-5 -12
-4 -5
-3 0
-2 3
-1 4
0 3
1 0
2 -5
3 -12
Plot the points and joint them to make a curve.
Refer the attached figure below.
#Learn more
Draw the graph of polynomial f(X)=x^2-2x-8
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