# Finding the Quadratic of a Graph using Tangents

• healey.cj
In summary, the conversation discusses a quadratic equation assignment where a cup of hot coffee is left to cool over a 50 minute period. The equation needs to be derived from three points on a Cartesian plane and the data is given in a table with time and temperature values. The conversation also mentions plotting a time versus temperature graph and finding the rate of change or gradient at three different points. The person asking for help is not looking for someone to solve the problem for them, but rather asking for guidance on how to approach the problem.
healey.cj
Hey everyone,

We've been covering tangents and derivatives etc in class recently but there is a question on the assignment that we've been given that i don't know how to do.

The question is:
"A quadratic equation can be fitted to any three points on a cartesian plane. The model for such an equation in y=ax + bx+ c. By substitution three separate points (The first, middle and last data points) derive the equation of the Quadratic function that models the data."

The situation is a cup of hot coffee is left to cool over a 50 minute period and we have been given this table of values:

mins : Degrees Celcius
0 :83
5 :76.5
8 :70.5
11:65
15:61
18:57.5
24:52.5
35: 51
30:47.5
34:45
38:43
42:41
45:39.5
50:38

From there i have plotted the time vs. temp graph and attached 3 tangents to points time (t) = 0, t = 25 & t = 50.

at t=0 the Rate of Change or gradient was -1.85Degrees/min
at t=25, the ROC or Gradient was -0.92degrees/min
at t=50, the ROC or Gradient was -0.13degrees/min

I'm not asking for you to do this for me, I am just asking for the path i need to take or an idea of what i need to do...

Thanks everyone,
Chris

Come on guys, just steer me in the right direction...Please

## 1. What is the main purpose of finding the quadratic of a graph using tangents?

The main purpose of finding the quadratic of a graph using tangents is to determine the point at which the graph changes direction, known as the vertex. This can help us understand the behavior of the graph and make predictions about its future values.

## 2. How do you find the quadratic of a graph using tangents?

To find the quadratic of a graph using tangents, you need to first identify two points on the graph where the tangent lines intersect. Then, use the slope formula to calculate the slope of each tangent line. Finally, use the slope values to solve for the x-coordinate of the vertex using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation.

## 3. What is the significance of the vertex in a quadratic graph?

The vertex is significant in a quadratic graph because it represents the minimum or maximum point on the graph. This point is important because it tells us the highest or lowest value that the graph can reach, as well as the point at which the graph changes direction.

## 4. Can you find the quadratic of a graph using tangents if there is no vertex present?

No, you cannot find the quadratic of a graph using tangents if there is no vertex present. The vertex is a necessary component in this method of finding the quadratic, as it provides the x-coordinate for the calculation.

## 5. Are there any limitations to finding the quadratic of a graph using tangents?

Yes, there are some limitations to this method. It can only be used to find the quadratic of a graph if the graph is a perfect parabola, meaning it has no other curves or bends. Additionally, the method may not work for graphs with limited data points or those with very steep slopes.

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