Question

2 Draw the graph of y=x²-x-2 and hence solve
x2 -x-2=0
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Answer 1

Step-by-step explanation:

y = x²-x-2 is a quadratic eqn therefore it's graph will be a parabola

Step1 : Find the y- intercept

y=0-0-2

y=-2

y-intercept =(0,-2)

Step2: Find x-intercepts

x²-x-2=0

x²-2x+x-2=0

on solving we get

x=2 or x=-1

therefore, x-intercepts: (2,0) and (-1,0)

Step3 : Find the vertex

since a parabola is symmetric therefore the line of symmetry can be determined by taking the average of the x-intercepts

x =(2+(-1))/2

x = 0.5

Substitute this value of x in the given eqn to find the y coordinate

y=(0.5)² - 0.5 - 2

y = -9/4

y= - 2.25

therefore, coordinates of vertex :- (0.5, -2.25)

Step4: Extra point

Let x= -2

it implies y=(-2)² +2 -2 =4

hence coordinate of extra point(-2,4)

Now the graph is shown in the picture

For finding the roots

equate

x²-x-2=0

x²-2x+x-2=0

x(x-2)+1(x-2)=0

(x+1)(x-2)=0

x=-1 or x=2