Answer:
As the points are collinear, the slope of the line joining
any two points, should be same as the slope of the line joining two other
points.
Slope of the line passing through points (x
1
,y
1
) and (x
2
,y
2
) =
x
2
−x
1
y
2
−y
1
So, slope of the line joining (p,0),(0,q)= Slope of the line joining
(0,q) and (1,1)
0−p
q−0
=
1−0
1−q
−
p
q
=1−q
Dividing both sides by q,
−
p
1
=
q
1
−1
=>
p
1
+
q
1
=1
I believe it's A. Day 1 decreased by half from 8 would be 4. Day 2 decreased by half from 4 would be 2. Day 3 decreased by half from 2 would be 1. then .5 would be decrease by. 25, which would be .75. I hope that makes sense:)
The simple/ <span>common sense method:
</span>The typical lay out of a quadratic equation is ax^2+bx+c
'c' represents where the line crosses the 'y' axis.
The equation is only translated in the 'y' (upwards/downwards) direction, therefore only the 'c' component of the equation is going to change.
A translation upwards of 10 units means that the line will cross the 'y' axis 10 places higher.
9+10=19,
therefore <u>c=19</u>.
The new equation is: <u>y=x^2+19 </u>
<span>
<span>The most complicated/thorough method:
</span></span>This is useful for when the graph is translated both along the 'y' axis and 'x' axis.
ax^2+bx+c
a=1, b=0, c=9
Find the vertex (the highest of lowest point) of f(x).
Use the -b/2a formula to find the 'x' coordinate of your vertex..
x= -0/2*1, your x coordinate is therefore 0.
substitute your x coordinate into your equation to find your y coordinate..
y= 0^2+0+9
y=9.
Your coordinates of your vertex f(x) are therefore <u>(0,9) </u>
The translation of upward 10 units means that the y coordinate of the vertex will increase by 10. The coordinates of the vertex g(x) are therefore:
<u>(0, 19) </u>
substitute your vertex's y coordinate into f(x)
19=x^2+c
19=0+c
c=19
therefore <u>g(x)=x^2+19</u>
