For the function, tell whether the graph opens up or opens down, identify the vertex, and tell whether the graph is wider, narro
2 answers:
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Answer:
(d) opens up, (1, -3), narrower
Step-by-step explanation:
The factor of +2 multiplying the function tells you the graph is expanded vertically by a factor of 2. The parent function opens upward, and the positive sign on this expansion factor does not change that. The expansion means that y-values will be farther from the vertex for the same x-value distance from the vertex. This give the appearance of a narrower graph.
As always, the transformation ...
f(x -h) +k
moves the vertex from (0, 0) to (h, k). Here, you have (h, k) = (1, -3), so that is the location of the vertex of the transformed function.
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We have that
<span>A(-6,-5) and B (4,0)
we know that
</span><span>AP:PB is 2:3
so
(2+3)=5
AP=2/5
PB=3/5
step 1
find the x coordinate of P
Px=Ax+AP*ABx
where
Ax is the x coordinate of A
AP is 2/5
ABx is the distance AB in the x coordinate
so
PX=[-6+(2/5)*(4+6)]------>Px=-2
</span>step 2
find the y coordinate of P
Py=Ay+AP*ABy
where
Ay is the y coordinate of A
AP is 2/5
ABy is the distance AB in the y coordinate
so
Py=[-5+(2/5)*(0+5)]------>Py=-3
the point P is (-2,-3)
see the attached figure
<span>A(-6,-5) and B (4,0)
we know that
</span><span>AP:PB is 2:3
so
(2+3)=5
AP=2/5
PB=3/5
step 1
find the x coordinate of P
Px=Ax+AP*ABx
where
Ax is the x coordinate of A
AP is 2/5
ABx is the distance AB in the x coordinate
so
PX=[-6+(2/5)*(4+6)]------>Px=-2
</span>step 2
find the y coordinate of P
Py=Ay+AP*ABy
where
Ay is the y coordinate of A
AP is 2/5
ABy is the distance AB in the y coordinate
so
Py=[-5+(2/5)*(0+5)]------>Py=-3
the point P is (-2,-3)
see the attached figure