# Step-by-Step Guide to Solving a Challenging Equation - Homework Help

• thomas49th
In summary, the conversation discusses solving an equation in the form of S = at^2 + bt + c using given values for t and S. The solution process involves setting up and solving three equations, with the help of the given values for t, to find the values of a, b, and c. It is concluded that c must be equal to 0 and this knowledge can be used to simplify the other two equations.
thomas49th

## Homework Equations

As in the image above

## The Attempt at a Solution

I had a go but i rubbed it off the sheet.

Can someone take me through this step by step on how to solve it

Thanks

What is your question? You are told exactly what to do!

You are told that the equation must be of the form
S= at2+ bt+ c.

You are given t and S values for 6 different values of t.
Putting the given x and t values into the equation above for 3 different values of t (t= 0, 2, 3, as they suggest, will do but the choice is yours) will give you 3 equations to solve for a, b, and c. (Taking t= 0 will get an especially easy equation!)

so

t=0: 0 = 0 + 0 + 0 (c will have to be 0 if a and b are)
t=1: 10 =a+b+c
t=2: 30 =4a+2b+c
is that right?

Last edited:
thomas49th said:
so

t=0: 0 = 0 + 0 + 0 (c will have to be 0 if a and b are)

but where does it say a and b are 0?

t=0: 0 = a.0 + b.0 +c and hence c=0

the other equations are correct

if t = 0
then a x t = 0
b x t = 0
so c must be 0 if the equation equals 0

Correct. Now use that you know c=0 in the other two equations

Huh? I thought the other 2 equations were right?

t=0: 0 = 0a + 0b + 0
t=1: 10 =a+b+c
t=2: 30 =4a+2b+c

cant I right them as that?

Yes they are correct but you now know that c = 0

so a+b+c=a+b

and

4a+2b+c=4a + 2b

## 1. What is the equation that you are stuck on?

The equation that I am currently stuck on is a quadratic equation: y = ax^2 + bx + c. I am trying to solve for the values of a, b, and c.

## 2. What is the purpose of this equation?

The purpose of this equation is to find the solutions or roots of a quadratic function. It is often used in mathematics and physics to solve problems involving parabolic curves.

## 3. What are the steps to solve a quadratic equation?

To solve a quadratic equation, you can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. First, determine the values of a, b, and c in the equation. Then, plug those values into the formula and simplify to find the solutions for x.

## 4. What should I do if I am stuck on a particular step in solving this equation?

If you are stuck on a particular step in solving the equation, try breaking it down into smaller parts and solving them one at a time. You can also ask a friend or teacher for help, or look for online resources or tutorials.

## 5. How can I check if my solution to the equation is correct?

You can check your solution by plugging in the values of a, b, and c into the original equation and seeing if it satisfies the equation. You can also use a graphing calculator to graph the equation and see if the solutions you found are the x-intercepts of the graph.

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