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Determining the equation of the parabola

Find the equation of the parabola with the vertex of (2,0) and focus of (2,2)

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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"

Posted on Jan 10, 2009

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How do I solve (3x-2y)2(3xy-3)


First, we will find y in terms of x. We will use the first equation to determine this.
4x+2y=2
We can subtract 4x from both sides:
2y=2-4x
And then divide both sides of the equation by two:
y=1-2x
Since we now have y in terms of x, we can substitute this into our second equation.
-3x-y=-3
-3x-(1-2x)=-3
Then, we can distribute the minus sign
-3x-1+2x=-3
-x-1=-3
Next, we can add 1 to both sides of the equation.


-x=-2
Finally, we divide both sides by negative one to isolate x.
x=2
Now that we have x's value, we can find y's value.
The first thing that we determined is:
y=1-2x
We can substitute in the value of x to this equation.
y=1-2x
plot-formula.mpl?expression=y=1-2%2a2&x=0003
y=1-4
y=-3
Therefore, we now have the values of both variables.
x=2
y=-3

Jan 13, 2015 | SoftMath Algebrator - Algebra Homework...

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Write an equation in standard form for vertex(6,1) passing through the point (4,5)


Assuming the 'standard form' is "slope-intercept", calculate the slope from the equation m = y2-y1 = 5 - 1 = 4 = -2
x2-x1 4 - 6 -2
The intercept can be found by substituting either of the two points into the equation y = mx + b
5 = (-2)4 + b
5 = (-8) + b
13 = b
(OR, using the other point, y = mx + b
1 = (-2)6 + b
1 = (-12) + b
13 = b )
Then expressing in general:
y = (-2) x + 13

Oct 10, 2014 | Educational & Reference Software

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Chacha answers


It seems to me that you are trying to solve the quadratic equation
aX^2+bX+c=10 with a=-3, b=3, c=15 or -3X^2+3X+15=0.
Since the all the coefficients are multiples of 3, one can simplify the equation by dividing every thing by 3, leaving -X^2+X+5=0. But to avoid confusing you I will consider the original equation -3X^2+3X+15=0..
You must first find out if the equation has any real solutions. To do that you calculate the discriminant (you do not have to remember the name if you choose to).
Discriminant is usually represented by the Greek letter DELTA (a triangle)
DELTA =b^2-4*a*c =(3)^2-4*(-3)*(15)=189
If the discriminant is positive (your case) the equation has two real solutions which are given by
Solution1 =X_1=(-3-SQRT(189))/(-2*3)=(1+SQRT(21))/2
Solution2 =X_2=(-3+SQRT(189))/(-2*3)=(1-SQRT(21))/2 or about -1.791287847
Here SQRT stands for square root.

Aug 17, 2014 | Educational & Reference Software

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Khan academy


Since you have the coordinates of the three vertices, the most straightforward method is to calculate the length of the sides using the distance formula
d(P_1,P_2)=SQRT((X_1-X_2)^2+(Y_1-Y_2)^2)
where SQRT is the square root function, X_1, Y_1) are the coordinates of point P_1, etc.
With the three lengths available, use Heron's (sometimes called Hero's) to find the area.
Here is Heron's formula.
Let's call the lengths a, b, and c
Let p be the semi-perimeter p= (a+b+c)/2
Then
Area= SQRT [ p(p-a)(p-b)(p-c) ]
Make sure that there is a matching ) parenthesis to the one in the SQRT.

Alternatively,
You can choose the base as the side opposite the vertex (0,0)
Calculate the equation of the line that supports the base.
Calculate the equation of the line issuing from (0,0) and perpendicular t the base.
Calculate the coordinates of the intersection point , call it H, of the base and its perpendicular line (coming from (0,0)).
Calculate the distance OH, that is the height relative to the chosen base.
Use the formula Area= base*height/2

Now it is up to you to choose one of the two methods and calculate the area of that triangle. The second method involves more calculations than the first, and more possibilities of errors. Good Luck

Nov 06, 2013 | Mathsoft Educational & Reference Software

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What is the area of the triangle with vertices (0,0),(-3,5),(2,-7)


Since you have the coordinates of the three vertices, the most straightforward method is to calculate the length of the sides using the distance formula
d(P_1,P_2)=SQRT((X_1-X_2)^2+(Y_1-Y_2)^2)
where SQRT is the square root function, X_1, Y_1) are the coordinates of point P_1, etc.
With the three lengths available, use Heron's (sometimes called Hero's) to find the area.
Here is Heron's formula.
Let's call the lengths a, b, and c

Let p be the semi-perimeter p= (a+b+c)/2
Then
Area= SQRT [ p(p-a)(p-b)(p-c) ]
Make sure that there is a matching ) parenthesis to the one in the SQRT.

Alternatively,
You can choose the base as the side opposite the vertex (0,0)
Calculate the equation of the line that supports the base.
Calculate the equation of the line issuing from (0,0) and perpendicular t the base.
Calculate the coordinates of the intersection point , call it H, of the base and its perpendicular line (coming from (0,0)).
Calculate the distance OH, that is the height relative to the chosen base.
Use the formula Area= base*height/2

Now it is up to you to choose one of the two methods and calculate the area of that triangle. The second method involves more calculations than the first, and more possibilities of errors. Good Luck

Nov 06, 2013 | The Learning Company Achieve! Math &...

1 Answer

What are the equations and its kinds?


Definition



A mathematical statement used to evaluate a value. An equation can use any combination of mathematical operations, including addition, subtraction, division, or multiplication. An equation can be already established due to the properties of numbers (2 + 2 = 4), or can be filled solely with variables which can be replaced with numerical values to get a resulting value. For example, the equation to calculate return on sales is: Net income รท Sales revenue = Return on Sales. When the values for net income and sales revenue are plugged into the equation, you are able to calculate the value of return on sales.

There are many types of mathematical equations.

1. Linear Equations y= mx + b (standard form of linear equation)
2. Quadratic Equations y= ax^2+bx+c
3. Exponential Equations y= ab^x
4. Cubic Equations y=ax^3+ bx^2+cx+d
5. Quartic Equations y= ax^4+ bx^3+ cx^2+ dx+ e
6. Equation of a circle (x-h)^2+(y-k)^2= r^2
7. Constant equation y= 9 (basically y has to equal a number for it to be a constant equation).
8. Proportional equations y=kx; y= k/x, etc.



Jun 14, 2011 | Educational & Reference Software

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What causes some parabolas to have no x-intercepts?


If the parabola has its concavity turned downward and it maximum value is lower than 0 then the value of the functions are always negative (never reach 0).
Similarly, if the parabola has it concavity turned upward, and its minimum value is positive, then all the values of the functions are positive (never reach zero). Thus if y is never equal to zero the function has no x intercepts.
The concavity is called by some people the mouth.

Aug 20, 2010 | SoftMath Algebrator - Algebra Homework...

2 Answers

4 spoons and 3 forks cost $15. 4 spoons and 1 fork cost $13. Find the cost of five forks.


Hi romanam
If spoon is "s" and fork is "f"
you get 2 equations like:
4s + 3f = 15 equation 1
4s + 1f = 13 equation 2
Equation (1) - equation (2) gives :
2f = 2 which means
1f = 1 (dividing both sides by 2)
! fork costs $1
5 forks cost $5
If you are happy with the answer, please give a rating
luciana44


Oct 08, 2009 | The Learning Company Achieve! Math &...

1 Answer

Find the equation of the ellipse whose center is at (0,0), one vertex is at (3,0) and one end of minor axis is at(0,2)


find the volume of the largest cylinder with circular base that can be incribed in a cube whose volume is 27cu.in?

Mar 18, 2009 | Educational & Reference Software

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