Graph the quadratic functions y = -2x^2 and y = -2x^2 + 4 on a separate piece of paper. Using those graphs, compare and contrast
the shape and position of the graphs
Have tried to understand this, all I know is after finding the position for -2x^2, the -2x^2+4 will just move upwards by 4.
Real answers please :)
Have tried to understand this, all I know is after finding the position for -2x^2, the -2x^2+4 will just move upwards by 4.
Real answers please :)
1 answer:
Answer:
They are represented by downward parabola
They have the same equations of line of symmetry
Their vertices have same x-coordinates but different y-coordinates
They have the same domains
They have different ranges
They have different maximum values at same x values
The graph of y = -2x² + 4 is the image of the graph y = -2x² after translation 4 units up
Step-by-step explanation:
y = -2x² is a quadratic equation which represents by a parabola
From the red graph:
The graph of y = -2x² is represented by downward parabola
It has a maximum vertex (0 , 0)
The line of symmetry at x = 0
Its maximum value = 0 at x = 0
Its domain is {x: x ∈ R}
Its range is {y: y ≤ 0}
From the blue graph:
The graph of y = -2x² + 4 is represented by down ward parabola
It has a maximum vertex (0 , 4)
The line of symmetry at x = 0
Its maximum value = 4 at x = 0
Its domain is {x: x ∈ R}
Its range is {y: y ≤ 4}
From the two graphs
They are represented by downward parabola
They have the same equations of line of symmetry
Their vertices have same x-coordinates but different y-coordinates
They have same domains
They have different ranges
They have different maximum values at same x values
The graph of y = -2x² + 4 is the image of the graph y = -2x² after translation 4 units up
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Answer:
The probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.
Step-by-step explanation:
The random variable <em>T</em> is defined as the amount of time a customer spends in a bank.
The random variable <em>T</em> is exponentially distributed.
The probability density function of a an exponential random variable is:
The average time a customer spends in a bank is <em>β</em> = 10 minutes.
Then the parameter of the distribution is:
An exponential distribution has a memory-less property, i.e the future probabilities are not affected by any past data.
That is, <em>P</em> (<em>X</em> > <em>s</em> + <em>x</em> | <em>X</em> ><em> s</em>) = <em>P</em> (<em>X</em> > <em>x</em>)
So the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is:
P (X > 15 | X > 10) = P (X > 5)
Thus, the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.