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About hyperbola transverse axis on the y-axis, slope of asymptote numerically equal to nine-tenths of the conjugate axis,one vertex at (0,-9).

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I am not quite sure how the major axis of your hyperbola is directed and i do not know if the lengths you give are measures of the major and minor axes or the measures of the semi-major and semi-minor axes. So I am giving you the equations and the graphs so that you can decide for yourself what is appropriate for your problem.

Major axis parallel to the X-axis
Equation and graph

k24674_37.jpgk24674_38.jpg
Center is at x=1 and y=-2, semi-major axis length is a=6, and semi-minor axis length is b=12


Major axis is parallel to the y-axis
Equation
k24674_39.jpgk24674_40.jpg

Center is at x=1 and y=-2, semi-major axis length is a=12, and semi-minor axis length is b=6.

I trust you can customize the equations to fit your need.

Posted on Mar 26, 2011

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Whats the answer to y=(x+2)^2 using a new equation in vertical form a transfer right 4 unit up 2 unit and reflect on x axis


Let's start with the original equation. It is in the form y=a(x-h)^2+k, where (h,k) is the vertex. In this case, h= - 2 and k= 0. Thus, is it y=x^2 and we have done a horizontal translation 2 units to the left. I assume we are going to translate this 4 units to the right, then 2 units up, and then reflect it in the x-axis. Before we do the reflection, we will be 2 units to the right and 2 units up. This equation would be y=(x-2)^2+2. If we reflect this in the x-axis, would we get a downward facing parabola y=-(x-2)^2 -2?

Good luck,

Paul

Dec 06, 2015 | Office Equipment & Supplies

1 Answer

How i can solve quadratic equations which have no real roots


If the quadratic equation has no roots, you cannot find the roots. The discriminate is negative, so if we attempt to use the quadratic equation, we get no roots.

For example, y=x^2 +0x + 3

a=1, b=0, c=3

(-b+/- sqrt(b^2 -4ac))/2a

Substituting in the numbers, we get

x= (-0 +/-sqrt(0^2 - 4(1)3))/2
x= (0 +/- sqrt (-12))/2

We cannot do the square root of -12. Therefore, there are no roots. This is the same as having no x-intercepts. The discriminant is b^2-4ac. In this case it is -12. Thus, there are no real roots.

However, you can still determine the maximum or minimum, the vertex, the axis of symmetry, the y-intercept and the stretch/compression. With this information you can graph the equation.

In this case, the y-intercept is 3, the vertex is at (0,3), the axis of symmetry is x=0, the minimum value of the function is 3.

Good luck.

Let me know if you have any questions.

Paul

Nov 04, 2015 | Casio FX991ES Scientific Calculator

1 Answer

How do I find a slope then describe what it means in terms of the rate of change of the dependent variable per unit of the change in the independent variable.


Slope is defined in many ways. Some use rise over run. y over x. delta y over delta x. I find the easiest way to find it is to draw a triangle to calculate the slope. I try and pick points on the line that go through the corners of the graph paper to more accurately measure the slope. The bigger the triangle the better. Now count the number of squares going up and down and the number of square going left to right. Divide the change in y by the change in x. This is your slope. If the line is going up to the right. the slope is positive. If it is going up to the left, the slope is negative.

"describe what it means in terms of the rate of change of the dependent variable per unit of the change in the independent variable."

If the y axis is distance and the x axis is time, the slope will be kilometers/hour, or speed, the rate of change.

Good luck.
Paul

Feb 24, 2015 | Office Equipment & Supplies

1 Answer

Y=-3/4x+13


Assuming we're dealing with the straight line y=(-3/4)x+13. the y intercept is 13.

If we're really dealing with the hyperbola y=-3/4x+13 then there is no y intercept since there's a vertical asymptote at x=0.

Mar 20, 2014 | Computers & Internet

1 Answer

What is the axis of symmetry of the function f(x) = x2 + 10x?


It is the vertical line that passes through the vertex of the parabola y=x^2+10x
You can graph the function or use differential calculus to find position of the minimum.
The vertex is at (-5,-25) and the axis of symmetry is the line x=-5.

Dec 19, 2013 | Office Equipment & Supplies

2 Answers

How many tenths there are in 11/2?


Just convert the 1 and 1/2 to a fraction and then multiply the top and bottom (numerator and denominator) by 5 to see that fraction in tenths.

Multiplying both the numerator and the demominator of a fraction by the same number does not change the value of the fraction.

1 1/2 is the same as 3 / 2

Now multiply both top and bottom by 5.

3 / 2 = 15 / 10


Therefore there are 15 tenths in 1 1/2.

Good luck I hope this helps.

Joe.

Sep 17, 2011 | Office Equipment & Supplies

1 Answer

Can i ask how to answer this?2x-4y-9=o


That is an equation describing a straight line. The "slope-intercept" form of a line is

y = mx + b

where m is the slope (change in y-value / change in x-value)
and b is the y-intercept (the point where the line crosses the y-axis when x=0)

Positive slope means the line is rising and negative slope means it's falling.

You can rewrite the original equation 2x - 4y -9 = 0 in slope-intercept form:

y = (1/2)x - (9/4)

So you know the slope is positive 1/2 (line rises 1 y-unit for each 2 x-unit change) and crosses the y-axis at -9/4. With this information you can graph the line.

Jul 12, 2011 | Sewing Machines

1 Answer

Find the equation of the hyperbola which satisfies the given equation center(1,-2) transverse axis to the x-axis transverse 6 and conjugate axis 12


I am not quite sure how the major axis of your hyperbola is directed and i do not know if the lengths you give are measures of the major and minor axes or the measures of the semi-major and semi-minor axes. So I am giving you the equations and the graphs so that you can decide for yourself what is appropriate for your problem.

Major axis parallel to the X-axis
Equation and graph

k24674_37.jpgk24674_38.jpg
Center is at x=1 and y=-2, semi-major axis length is a=6, and semi-minor axis length is b=12


Major axis is parallel to the y-axis
Equation
k24674_39.jpgk24674_40.jpg

Center is at x=1 and y=-2, semi-major axis length is a=12, and semi-minor axis length is b=6.

I trust you can customize the equations to fit your need.

Mar 24, 2011 | Office Equipment & Supplies

1 Answer

Determining the equation of the parabola


V (2,0) and Focus (2,2)
since the focus is 2 units above the vertex, the parabola opens upward

vertex (h,k)
a is the focal length (distance between the vertex and the focus)
a = 2
(2 units above the vertex)

(x-h)^2 = 4a (y-k)
(x-2)^2 = 4(2) (y-0)
x^2 - 4x + 4 = 8 (y)
x^2 - 4x + 4 = 8y
x^2 - 4x - 8y + 4 = 0

**Answer: "(x-2)^2 = 8 (y)" or in expanded form "x^2 - 4x - 8y +4"

Nov 18, 2008 | Super Tutor Trigonometry (ESDTRIG) for PC

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