Question

A) draw the graph of the relation y = x² - 2x -1 using scale of 2cm to 1unit on both axis

b) use the graph to find the roots of the equation x² - 2x -1 = 0
c)using the same axis, draw the graph of y=2x - 3
d) use your graph to solve simultaneously
y=x² - 2x - 1
y=2x - 3

Answer 1

See explanation and attachment

Explanation:

a) To graph
`y=x^2-2x-1`, we need to plot some few points.

When x=-2,
`y=(-2)^2-2(-2)-1=7` so we plot (-2,7).

When x=-1,
`y=(-1)^2-2(-1)-1=2` so we plot (-1,2)

When x=0,
`y=(0)^2-2(0)-1=-1` so we plot (0,-1)

When x=1,
`y=1^2-2(1)-1=-2` so we plot (1,-2)

When x=2,
`y=(2)^2-2(2)-1=-1` so we plot (2,-1)

We then draw a smooth curve through the points to obtain the curve in the attachment.

b) The graph intersected the x-axis (y=0) at x=-0.41 and x=2.41. These are the roots.

c) For the line y=2x-3

When x=0, y=2(0)-3=-3 so we plot (0,-3)

When x=1, y=2(1)-3=-1 So we plot (1,-1)

We draw a straight line through these two points to intersect the parabola as shown on the graph.

d) To solve

`y=x^2-2x-1`

and

`y=2x-3` simultaneously using the graph, we look for the point of intersection of the parabola and the straight line.

The solution is (0.59,-1.83) and (3.41,3.83)