Question

can anyone solve this with step by step explaination and graph​

Answer 1

Answer:

Graph and complete explanation is also attached for reference.

Answer 2

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

Given quadratic polynomial is

$\rm :\longmapsto\:p(x) = {x}^{2} + 3x - 4$

Let assume that

$\rm :\longmapsto\:y = p(x) = {x}^{2} + 3x - 4$

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

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

Here,

$\purple{\rm :\longmapsto\:a = 1}$

$\purple{\rm :\longmapsto\:b = 3}$

$\purple{\rm :\longmapsto\:c = - 4}$

So, on substituting the values, we get

$\rm :\longmapsto\: \:Vertex = \bigg( - \dfrac{ 3}{2} , \: \dfrac{ - 16 - 9 }{4} \bigg) = \bigg( - \dfrac{3}{2}, - \dfrac{25}{4} \bigg)$

Step :- 2 Point of intersection with x - axis

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

So, on substituting the value of y = 0 in given curve, we get

$\purple{\rm :\longmapsto\: {x}^{2} + 3x - 4 = 0}$

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

$\purple{\rm :\longmapsto\:x(x + 4) - 1(x + 4) = 0}$

$\purple{\rm :\longmapsto\:(x + 4)(x - 1) = 0}$

$\purple{\rm\implies \:x = - 4 \: \: or \: \: x = 1}$

Hence,

The point of intersection with x- axis is (1, 0) and ( - 4, 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

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

Hence, the point of intersection with y- axis is (0, - 4).

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 4 \\ \\ \sf 1 & \sf 0 \\ \\ \sf - 4 & \sf 0\\ \\ \sf - 1.5 & \sf - 6.25 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points.

➢ See the attachment graph.