Question about Super Tutor Trigonometry (ESDTRIG) for PC

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

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

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

y=1-4

y=-3

Therefore, we now have the values of both variables.

x=2

y=-3

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

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...

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**

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:

Oct 10, 2014 | Educational & Reference Software

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.

aX^2+bX+c=10 with a=-3, b=3, c=15 or

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

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

Here SQRT stands for square root.

Aug 17, 2014 | Educational & Reference Software

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

**
**

d(P_1,P_2)=SQRT(

where SQRT is the

With the three lengths available, use Heron's (sometimes called Hero's) to find the area.

Let's call the lengths

Let p be the semi-perimeter p= (a+b+c)/2

Then

Area= SQRT [

Alternatively,

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

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

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

d(P_1,P_2)=SQRT(

where SQRT is the

With the three lengths available, use Heron's (sometimes called Hero's) to find the area.

Let's call the lengths

Let p be the semi-perimeter p= (a+b+c)/2

Then

Area= SQRT [

Make sure that there is a matching ) parenthesis to the one in the SQRT.

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

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 &...

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

y = -0.5x^2 - 1.5x - 3

Feb 09, 2011 | Educational & Reference Software

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.

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).

The concavity is called by some people the mouth.

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

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

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 &...

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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