Question

Draw the Graph of x² - 2x - 8​

Answer 1

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• We are given the quadratic equation

$\LARGE{\bf{\underline{\underline{SOLUTION:}}}}$

Find the vertex.

to find the vertex, we know,

$\sf \to x=-\dfrac{b}{2a}$

Now in our equation, b is -2 and a is 1.

$\sf \to x=\dfrac{\not{2}}{\not{2}}$

$\sf \to x=1$

Therefore, our vertex is 1.

Now find the extremum.

Extremum = c - (b² / 4a).

= - 8 - (4 / 4)

= -9.

Therefore, our vertex is 1 and extremum is -9. Then the lowest point will be  => (1, -9).

Now just find the roots of the quadratic equation.

= x² - 2x - 8​ = 0

= x² +2x - 4x - 8 = 0

= x(x+2) -4(x+2) = 0

= (x-4)(x+2) = 0.

Therefore, x=4, x=-2. The points on the x-axis will be (-2,0) and (4,0).

To find the y-intercept substitute x=0 in given equation,

= 0²- 2(0)-8

= 8

∴ The y-intercept is (0,-8)

Now x² - 2x - 8​ is given. Write it as: y = x² - 2x - 8​. Now hit - and - trial and find the values of x and y.

Now we need to collect our points and plot it. We have:

• (1, -9).
• (-2,0)
• (4,0)
• (0,-8)

just plot these points on the graph.

See the file attached for graph.

There is another method.  Convert the equation as y = x² - 2x - 8​, find the values of x and y by hit - and - trail, then plot the points.

The values of x and y are:

$\begin{tabular}{ |c|c|} x & y \\ 1 & -9 \\ 2 & -8 \\ 3 & -5 \\ 4 & 0 \\5 & 7 \\6 & 16 \\\end{tabular}$

Now just plot these points in the graph.

Regards,

Sujal Sirimilla

Ex-brainly star.