Question

2x^2-4x draw the graph​

Answer 1

Answer:

pls.wait five to ten minutes

Answer 2

$\large\underline{\sf{Solution-}}$

Given polynomial is

$\rm :\longmapsto\:2 {x}^{2} - 4x$

Let we assume that

$\rm :\longmapsto\:f(x) \: = \: y \: = \: 2 {x}^{2} - 4x$

To plot the graph of the quadratic polynomial which is always parabola, the following steps have to be followed :-

Step :- 1 Vertex of parabola

We know, vertex of parabola of quadratic polynomial ax² + bx + c is given by

$\blue{ \boxed{\bf \:Vertex = \bigg( - \dfrac{ b}{2a} , \: \dfrac{4ac - {b}^{2} }{4a} \bigg)}}$

Here,

$\rm :\longmapsto\:a = 2$

$\rm :\longmapsto\:b = - \: 4$

$\rm :\longmapsto\:c = 0$

So, vertex of parabola is

$\rm :\longmapsto\:\ \:Vertex = \bigg( - \dfrac{ b}{2a} , \: \dfrac{4ac - {b}^{2} }{4a} \bigg)$

On substituting the values, we get

$\rm :\longmapsto\:\ \:Vertex = \bigg( - \dfrac{( - 4)}{2(2)} , \: \dfrac{4(2)(0)- {( - 4)}^{2} }{4(2)} \bigg)$

$\rm :\longmapsto\:\ \:Vertex = \bigg( 1 , \: - 2 \bigg)$

Step :- 2

Point of intersection with x - axis

We know, on x - axis, y = 0.

So, on substituting the value, we get

$\rm :\longmapsto\: {2x}^{2} - 4x = 0$

$\rm :\longmapsto\:2x(x - 2) = 0$

$\rm :\implies\:x = 0 \: \: \: or \: \: \: x = 2$

Hence, the point of intersection with x- axis is (0, 0) and (2, 0).

Now,

Point of intersection with y - axis.

We know, on y - axis, x = 0

So, on Substituting the value in given curve, we get

$\rm :\longmapsto\:y = 2 {(0)}^{2} - 4 \times 0 = 0$

Hence, the point of intersection with y- axis is (0, 0).

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 0 \\ \\ \sf 2 & \sf 0\\ \\ \sf 1 & \sf - 2 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.