Maths. Under functions on graphs of a parabola and a one to one function on the same set of axes when calculating the length how do i use the Turning point formula?
Please be more specific
To find the "length" of a parabola you will need to know integral calculus.
"turning point" formula of a parabola??
for any y = ax^2 + bx + c
the x of the vertex is -b/(2a), once you have the x
plug into the equation to get y
Ok thanks and Yep i also thought its calculus but some1 said its not so i got confused.
To find the length of a parabolic curve using the turning point formula, you will need to know the coordinates of the turning point. Once you have the coordinates, you can calculate the length using the distance formula.
Here's a step-by-step guide:
1. Determine the coordinates of the turning point of the parabola. The turning point is given by the formula:
- x-coordinate (vertex x) = -b/ (2a),
- y-coordinate (vertex y) = f(-b/ (2a)), where the quadratic equation is in the form of f(x) = ax^2 + bx + c.
2. Compute the x-value of the other point on the curve that you want to find the length to. Let's call this x-value "x2".
3. Calculate the corresponding y-value of the other point by substituting x2 into the quadratic equation: f(x2) = ax2^2 + bx2 + c. This will give you the y-coordinate of the point, which we will call "y2".
4. Apply the distance formula to calculate the length between the turning point and the other point on the curve:
- Distance (length) = sqrt((x2 - vertex x)^2 + (y2 - vertex y)^2)
By following these steps, you will be able to calculate the length between the turning point of a parabola and any other point on the curve.