The graphs below are both quadratic functions. The equation of the red graph is
1 answer:
Answer:
D.
Step-by-step explanation:
- The equation of the red quadratic graph is
.
- This is the parent quadratic function or the base of the quadratic functions.
- This red quadratic graph has been dilated by a certain scale factor to obtain the blue graph. Recall that, when the scale factor is a fraction, such that
the graph is stretched horizontally.
- The dilated graph then becomes wider than the parent function.
- From the given function equations, the possible value of k can only be
.
- Therefore the blue graph has equation:
- The correct answer is D.
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Answer:
Given :
ABC is a right triangle in which ∠ABC = 90°,
Also, Legs AB and CB are extended past point B to points D and E,
Such that,
To prove :
Proof :
In triangles AEC and EBA,
∠EAC= ∠ABE ( right angles )
∠CEA = ∠AEB ( common angles )
By AA similarity postulate,
,
Similarly,
Now, In triangles ADC and CBD,
∠ACD = ∠CBD ( right angles )
∠ADC= ∠BDC ( common angles )
By AA similarity postulate,
,
Similarly,
From equations (1) and (2),
The corresponding sides of similar triangles are in same proportion,
Hence, proved....
