MHB Quadratics: How to determine parabola equation.

  • Thread starter Thread starter James400
  • Start date Start date
  • Tags Tags
    Parabola
AI Thread Summary
To determine the equations of parabolas given specific points, intercepts, and vertexes, the vertex form of a parabola is utilized. For the first parabola with a turning point at (1,6) and passing through (-1,8), the equation can be expressed as y=a(x-1)²+6, where 'a' is calculated using the provided point. The second parabola has x-intercepts at 2 and 7, and passes through (3,6), requiring a different approach to find its equation based on the intercepts. The discussion emphasizes the importance of showing work and understanding the steps involved in deriving the equations. Overall, participants are encouraged to share their thought processes for better assistance.
James400
Messages
6
Reaction score
0
Hi all. I need a bit of help determining the equation of some parabolas given points, intercepts and vertexes. Below are the exacts questions, any help will be much appreciated as I need this done soon!

1. A parabola has turning point (1,6) and passes through the point (-1,8). Find its equation.

2. A parabola has x-intercepts of 2 and 7 and passes through the point (3,6). Find
the equation of the parabola.

Please show working out!
 
Mathematics news on Phys.org
James400 said:
Hi all. I need a bit of help determining the equation of some parabolas given points, intercepts and vertexes. Below are the exacts questions, any help will be much appreciated as I need this done soon!

1. A parabola has turning point (1,6) and passes through the point (-1,8). Find its equation.

2. A parabola has x-intercepts of 2 and 7 and passes through the point (3,6). Find
the equation of the parabola.

Please show working out!

My reply to your other post holds here too. Please consider posting some of your work, or letting us know what you don't understand.
 
I'm a little confused as to where to start as a matter of fact!:) I know the final objective is to reach the equation in standard form using the information provided, but I'm not sure how to do that (the processes involved). I was just hoping to get a step through of the processes required to reach the answer.
 
James400 said:
Hi all. I need a bit of help determining the equation of some parabolas given points, intercepts and vertexes. Below are the exacts questions, any help will be much appreciated as I need this done soon!

1. A parabola has turning point (1,6) and passes through the point (-1,8). Find its equation.

Since we are given the vertex, let's use the vertex form of a parabola:

$$y=a(x-h)^2+k$$

Since the vertex (turning point) is given as $(1,6)$, we may write:

$$y=a(x-1)^2+6$$

Now, to determine $a$, we may use the other given point $(-1,8)$ as follows:

$$y(-1)=a(-1-1)^2+6=8$$

Solving the above equation for $a$, what do you get?
 
MarkFL said:
Since we are given the vertex, let's use the vertex form of a parabola:

$$y=a(x-h)^2+k$$

Since the vertex (turning point) is given as $(1,6)$, we may write:

$$y=a(x-1)^2+6$$

Now, to determine $a$, we may use the other given point $(-1,8)$ as follows:

$$y(-1)=a(-1-1)^2+6=8$$

Solving the above equation for $a$, what do you get?

I'm all good with these questions now. I solved them a little while ago, but I'm still stuck on the other questions I posted.
 
Thread 'Video on imaginary numbers and some queries'

Thread 'Video on imaginary numbers and some queries'

Hi, I was watching the following video. I found some points confusing. Could you please help me to understand the gaps? Thanks, in advance! Question 1: Around 4:22, the video says the following. So for those mathematicians, negative numbers didn't exist. You could subtract, that is find the difference between two positive quantities, but you couldn't have a negative answer or negative coefficients. Mathematicians were so averse to negative numbers that there was no single quadratic...
View full post »
Thread 'Unit Circle Double Angle Derivations'

Thread 'Unit Circle Double Angle Derivations'

Here I made a terrible mistake of assuming this to be an equilateral triangle and set 2sinx=1 => x=pi/6. Although this did derive the double angle formulas it also led into a terrible mess trying to find all the combinations of sides. I must have been tired and just assumed 6x=180 and 2sinx=1. By that time, I was so mindset that I nearly scolded a person for even saying 90-x. I wonder if this is a case of biased observation that seeks to dis credit me like Jesus of Nazareth since in reality...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Similar threads

MHB Determine the equation of the parabola
Replies
1
Views
1K
MHB Parabola Tangent: GP Relation for Fixed Point Chords
Replies
4
Views
1K
MHB How to Find Lines Tangent to a Parabola Passing Through a Given Point?
Replies
1
Views
2K
MHB How to Determine the Vertex of a Parabola?
Replies
3
Views
3K
MHB Quadratic Equation Help: Find 3 Points to Determine Answer
Replies
6
Views
2K
MHB Parabola standard form of equation at x = -5
Replies
4
Views
3K
MHB Parabola standard form of equation at x = -1
Replies
2
Views
2K
Equation for a tilted parabola in 3D?
Replies
2
Views
3K
MHB Normals from a point to a parabola
Replies
7
Views
2K
Is there a formula for this parabola?
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top