Question

find the graph of X square+3x-4 and zeroes​

Answer 1

Answer:

zeros are

x = 1 ,x = -4 are the zeros of above equation

Answer 2

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

Given

$\: \: \: \: \: \: \: \: \bull \sf \: \:y = {x}^{2} + 3x - 4$

1. Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:y = {0}^{2} + 3 \times 0 - 4$

$\rm :\longmapsto\:y = 0 + 0 - 4$

$\bf\implies \:y \: = \: - \: 4$

2. Substituting 'x = 1' in the given equation, we get

$\rm :\longmapsto\:y = {1}^{2} + 3 \times 1 - 4$

$\rm :\longmapsto\:y = 1 + 3 - 4$

$\bf\implies \:y \: = \: \: 0$

3. Substituting 'x = 2' in the given equation, we get

$\rm :\longmapsto\:y = {2}^{2} + 3 \times 2 - 4$

$\rm :\longmapsto\:y = 4 + 6 - 4$

$\bf\implies \:y \: = \: \: 6$

4. Substituting 'x = - 1' in the given equation, we get

$\rm :\longmapsto\:y = {( - 1)}^{2} + 3 \times ( - 1) - 4$

$\rm :\longmapsto\:y = 1 - 3 - 4$

$\bf\implies \:y \: = \: - \: 6$

5. Substituting 'x = - 2' in the given equation, we get

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

$\rm :\longmapsto\:y = 4 - 6 - 4$

$\bf\implies \:y \: = \: - \: 6$

6. Substituting 'x = - 3' in the given equation, we get

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

$\rm :\longmapsto\:y = 9 - 9 - 4$

$\bf\implies \:y \: = \: - \: 4$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 4 \\ \\ \sf 1 & \sf 0 \\ \\ \sf 2 & \sf 6\\ \\ \sf - 1 & \sf - 6\\ \\ \sf - 2 & \sf - 6\\ \\ \sf - 3 & \sf - 4 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points and draw curve passing through these points with smooth hands. The curve thus obtained represents the graph of y = x² + 3x - 4. This curve is called Parabola whose turning point is called vertex of parabola.

➢ See the attachment graph

Observations :-

1. The coefficient of x² > 0, so the parabola y = x² + 3x - 4 is open upwards

2. The parabola cuts the x - axis at two distinct points (1, 0) and (- 4, 0). Therefore, the zeroes of polynomial are 1 and - 4.

3. Parabola is Symmetric along y - axis.