Order the group of quadratic functions from widest to narrowest graph. y = 6x2, y = −4.5x2, y = −x2
2 answers:
To solve this problem you must keep on mind the following information: By definition, a quadratic function has the following form:
Where
is the leading coefficient.
If the leading coeficient is closer to zero, the parabola is widest,if it has a larger positive or negative value, the parabola is narrowest.
Therefore, by knowing the information above, you have that the answer is:
Where
If the leading coeficient is closer to zero, the parabola is widest,if it has a larger positive or negative value, the parabola is narrowest.
Therefore, by knowing the information above, you have that the answer is:
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Answer:
C) The parabola is narrower and reflected across the x-axis.
Step-by-step explanation:
The original parabola has equation:
The transformed parabola has equation
How wide the graph is can be determined by the absolute value of the coefficient.
The smaller the absolute value of the coefficient, the wider the graph.
Since
The original graph is wider than the transformed graph.
Also the negative factor tells us there is a reflection in the x-axis.
Answer: The fire is 3.5 miles from tower B
Step-by-step explanation: Please refer to the attached diagram. The triangle in the attached diagram illustrates the clues given in the question. Both rangers are standing at points A and B respectively with a distance of 5 miles between them, which is line AB. Also, one ranger spots a fire from a tower at an angle of 42 degrees, which is point A. Another ranger spots the same fire from another tower, but from an angle of 64 degrees, which is point B. The fire is at point C on the triangle. Now we have a triangle with only one side known (5 miles) and three angles known (the third angle is computed as 180 - {64+42} which equals 74) which are 64 degrees, 42 degrees and 74 degrees.
The distance from the fire to tower B is calculated using the law of sines. (Note that this is not a right angled triangle, hence we cannot use trigonometric ratios). The law of sines is expressed as follows;
a/SinA = b/SinB or
a/SinA = c/SinC
Depending on the sides and angles we are given and the ones we are to calculate.
The distance from the fire to tower B is line BC, labeled as a in our diagram. Using the law of sines
a/SinA = c/SinC
(Note also that a is directly facing angle A, c is directly facing angle C, and so on)
a/SinA = c/SinC
a/Sin 42 = 5/Sin 74
By cross multiplication we now have
a (Sin 74) = 5 (Sin 42)
Divide both sides of the equation by Sin 74 and we now arrive at
a = 5 (Sin 42)/Sin 74
a = 5 (0.6691)/0.9613
a = 3.3455/0.9613
a = 3.4802
{rounded to the nearest tenth of a mile, a equals 3.5}
Therefore the distance from tower B to the fire is approximately 3.5 miles
