Question

The equation y=2x^2 + 4x + 17 is in the form of a( x + b)^2+c.

Sketch the graph.​

Answer 1

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

The given equation is

$\rm :\longmapsto\:y = {2x}^{2} + 4x + 17$

$\rm :\longmapsto\:y = {2x}^{2} + 4x + 2 + 15$

$\rm :\longmapsto\:y = 2( {x}^{2} + 2x + 1) + 15$

$\rm :\longmapsto\:y = 2(x + 1)^{2} + 15$

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

$\rm :\longmapsto\:y = 2 {(0 + 1)}^{2} + 15$

$\rm :\longmapsto\:y = 2 + 15$

$\bf :\implies\:y = 17$

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

$\rm :\longmapsto\:y = 2 {(1 + 1)}^{2} + 15$

$\rm :\longmapsto\:y = 2 \times 4 + 15$

$\rm :\longmapsto\:y = 8 + 15$

$\bf\implies \:y = 23$

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

$\rm :\longmapsto\:y = 2 {( - 1 + 1)}^{2} + 15$

$\rm :\longmapsto\:y = 2 \times 0 + 15$

$\rm :\longmapsto\:y = 15$

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

$\rm :\longmapsto\:y = 2 {(2 + 1)}^{2} + 15$

$\rm :\longmapsto\:y = 2 \times 9 + 15$

$\rm :\longmapsto\:y = 18 + 15$

$\bf\implies \:y = 33$

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

$\rm :\longmapsto\:y = 2 {( - 2 + 1)}^{2} + 15$

$\rm :\longmapsto\:y = 2 + 15$

$\bf\implies \:y = 17$

Hᴇɴᴄᴇ,

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

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 17 \\ \\ \sf 1 & \sf 23 \\ \\ \sf 2 & \sf 33\\ \\ \sf - 1 & \sf 15\\ \\ \sf - 2 & \sf 17 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points

➢ See the attachment graph.