Beginning Algebra help - Intercepts (conic section)

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LINDAJOSEY

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How many x intercepts and y intercepts does the following equation have?

y2=25x2- 20x + 4

The problem is y squared equals 25x squared minus 20x plus 4
 
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LINDAJOSEY said:
How many x intercepts and y intercepts does the following equation have?

y2=25x2- 20x + 4

The problem is y squared equals 25x squared minus 20x plus 4
Click to expand...
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem
 
An "x-intercept" is where y= 0 so 25x^2- 20x+ 4= 0. Can you solve that quadratic equation?
A "y-intercept" is where x= 0 so y^2= 4.
 
Hi Linda. The exercise you've posted asks for the number of intercepts. You don't need to find the actual intercept values.

Do you know how many solutions there are for an equation of this form?

y^2 = positive constant​

For the number of x-intercepts, have you learned about the 'discriminant' for a quadratic polynomial (ax^2+bx+c)?

The discriminant is the number given by: b^2 - 4ac

Its sign (positive, negative, none) gives us information about the type of roots, including the number of x-intercept(s).

?
 
HallsofIvy said:
An "x-intercept" is where y= 0 so 25x^2- 20x+ 4= 0. Can you solve that quadratic equation?
A "y-intercept" is where x= 0 so y^2= 4.
Click to expand...
two questions here. this is an interesting post.
Can i solve it as a system of quadratic equations, as in,
25x^2- 20x+ 4= 0
y^2=4 ?
second question: do i need to factor y^2=4 before i do the system?.
thanks
 
eddy2017 said:
two questions here. this is an interesting post.
Can i solve it as a system of quadratic equations, as in,
25x^2- 20x+ 4= 0
y^2=4 ?
second question: do i need to factor y^2=4 before i do the system?.
thanks
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You are taking a WRONG approach!

We have only ONE equation, for each SEPARATE condition (NOT simultaneous)

25x^2- 20x+ 4= 0 ......................................... for x-intercept

Then we consider totally different condition (y-intercept) and get

y^2 = 4 ......................................... for y-intercept

These do not happen simultaneously - hence not simultaneous-equations.

We DO NOT have system of simultaneous equations!!

We have to solve these two equations separately !!
 
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Eddy

[MATH]y^2 = 25x^2 - 20x + 4[/MATH]
is not an equation to be solved. It is a relationship between two variables.

Now when we ask a question like “Are there any values of x for which y = 0 and if so where are they,”
we answer it by solving the equation below

[MATH]25x^2 - 20x + 4 = 0[/MATH],

which is an equation in one unknown, not a system of equations. The relationship is general, but the equation is specific.

Similarly, when we ask the question, “what values can y have if x = 0,” we answer it by solving the equation

[MATH]y^2 = 25*0^2-20*0+4,[/MATH]
which again is an equation in one unknown, not a system of equations. The specific equation lets us answer a specific question about a general relationship.
 
i get it now. the topic is really interesting and intriguing at the same time. i am going to study it and try to solve it if i may.
if following other's people ops is not in keeping with the forum rules, pls let me know. i hate to see good posts go to waste, unanswered!.
 
i understand it better after your explanation
The intercepts of a graph are points at which the graph crosses the axes. the x-intercept is the point at which the graph crosses the x-axis. here the y-coordinate is zero, and the y-intercept is the point at which the graph crosses the y-axis, here the x-coordinate is zero. i understand now why hallsoflvy equaled them to 0 at the beginning of the post.
To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.
do you mind if i give it a shot, i mean, at solving the two equations separately. i wanna know where you're going with this, like, when they're solved, what will the solutions indicate?. that would be interesting. if you allow me i will pursue this till the end.
 
eddy2017 said:
i understand it better after your explanation
The intercepts of a graph are points at which the graph crosses the axes. the x-intercept is the point at which the graph crosses the x-axis. here the y-coordinate is zero, and the y-intercept is the point at which the graph crosses the y-axis, here the x-coordinate is zero. i understand now why hallsoflvy equaled them to 0 at the beginning of the post.
To determine the x-intercept, we set y equal to zero and solve for x. Similarly, to determine the y-intercept, we set x equal to zero and solve for y.
do you mind if i give it a shot, i mean, at solving the two equations separately. i wanna know where you're going with this, like, when they're solved, what will the solutions indicate?. that would be interesting. if you allow me i will pursue this till the end.
Click to expand...
Go for it.

Notice the words in the title: conic sections
 
good morning, i am reporting my work on t he two equations back to you for consideration. sorry for the delay. it was evening when i started working on this and i had dinner and after dinner i always rest.
i am gonna attach my work on the two equations
for the first one i went with the quadratic formula which i think it is the easiest path
the second was not difficult at all.
i found one solution, or one x intercept from the first equation.
i found two solutions for the y intercept.
i do not know if there can be two y intercepts. or it's either or.
i know you will clear that up for me.
 

Attachments

  • finding how many x and y interecept there are in....pdf
    428.8 KB · Views: 5
i see that te pdf is not opening so i am going to take a screen shot and paste it here. i typed some things in math type and the page here does not accept that format. i need to learn to use latex but do not where the button here for latex is.

1625407947644.png

1625407977438.png
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You did both correctly. Nicely done.

If we were discussing a function, there could be only one y-intercept.

But the conic sections are not functions. Each is a so-called locus of points, which can have any number of y-intercepts.
 
JeffM said:
You did both correctly. Nicely done.

If we were discussing a function, there could be only one y-intercept.

But the conic sections are not functions. Each is a so-called locus of points, which can have any number of y-intercepts.
Click to expand...
i will devote a coupe of hours today to study what you told me to. the conic sections. if you can reccomend a good tutorial send it pls. thanks for all your help.
 
eddy2017 said:
i will devote a coupe of hours today to study what you told me to. the conic sections. if you can reccomend a good tutorial send it pls. thanks for all your help.
Click to expand...
The conic sections were originally studied as geometric objects, as the curves where a plane intersects a hollow right cone, over 2500 years ago. You can easily create them using a lamp with a lampshade and a wall in a dark room.

In the 17th century, with the development of analytic geometry, they were studied algebraically. They arise in nature all over the place.

www.khanacademy.org

Conic sections | Precalculus | Math | Khan Academy

When we slice a cone, the cross-sections can look like a circle, ellipse, parabola, or a hyperbola. These are called conic sections, and they can be used to model the behavior of chemical reactions, electrical circuits, and planetary motion.
www.khanacademy.org www.khanacademy.org
 
JeffM said:
The conic sections were originally studied as geometric objects, as the curves where a plane intersects a hollow right cone, over 2500 years ago. You can easily create them using a lamp with a lampshade and a wall in a dark room.

In the 17th century, with the development of analytic geometry, they were studied algebraically. They arise in nature all over the place.

www.khanacademy.org

Conic sections | Precalculus | Math | Khan Academy

When we slice a cone, the cross-sections can look like a circle, ellipse, parabola, or a hyperbola. These are called conic sections, and they can be used to model the behavior of chemical reactions, electrical circuits, and planetary motion.
www.khanacademy.org www.khanacademy.org
Click to expand...
thanks a million!
 
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