Answer:
A) (0,-8), B (4,0)
B) 2
C) y = 2x -8
Step-by-step explanation:
Given
[tex]y = x^2 -2x -8[/tex]
calculate the coordinate of point A and B
for point A
Point A lies on y axis, so for point A, coordinate of X axis is 0.
we will put x = 0 in the given equation
[tex]y = x^2 -2x -8[/tex] to find y.
[tex]y = 0^2 -2*0 -8 = -8[/tex]
Thus, y coordinate of point A is -8.
Thus, coordinate of point A (0, -8)
Point B lies on x axis, so for point B, coordinate of Y is 0.
we will put y = 0 in the given equation
[tex]y = x^2 -2x -8[/tex] to find x.
[tex]0= x^2 -2x -8\\=>x^2 -4x +2x -8 = 0\\=> x(x-4) +2(x-4) = 0\\=> (x+2)(x-4) = 0\\[/tex]
Thus x+2 = 0 or x-4 = 0
x = -2 or x = 4
but x cannot be -2 as x is on positive side of x axis, hence x can take only positive value
Thus, X coordinate of point B is 4
Thus, coordinate of point B(4, 0).
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The gradient of of two points (x1, y1) and (x2,y2) is given by
gradient = (y2-y1)/(x2-x1)
Since we have point A and B as (0, -8) and (4,0)
Thus gradient = 0 -(-8)/4-0) = 8/4 = 2 (answer B)
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Equation of straight line in point slope form is given by
y = mx +c
where m is the gradient of line and
c is y intercept .
Y intercept is point on y axis where the straight line meets y axis.
As calculated above
We have gradient = 2
c = -8 (co-ordinates of point A is only the y intercept)
Thus, equation of line AB
is y = 2x -8 Answer C.
