Question

How to find the equation of a parabola with 2 points and a linear line?

Answer 1

To find the equation of a parabola with 2 points and a linear line, you can find the slope of the linear line, use the slope-intercept form to find the y-intercept, and then substitute the values into the general equation of a parabola to solve for a and b.

Step-by-step explanation:

To find the equation of a parabola with 2 points and a linear line, we can start by finding the slope of the linear line using the formula:

Slope (m) = (Y₂ - Y₁) / (X₂ - X₁)

Next, we can use the slope-intercept form of a linear equation, y = mx + b, and substitute one of the given points to find the value of b (the y-intercept).

Once we have the slope (m) and the y-intercept (b), we can substitute them into the general equation of a parabola, y = ax + bx², and solve for the values of a and b using the other given point. This will give us the equation of the parabola.

Answer 2

To find the equation of a parabola using 2 points and a linear line, we go back to the standard form of the parabola which is (y-k)^2 = 4a (x-h)^2 or (x-h)^2 = 4a (y-k)^2 depending on the opening of the parabola. Using two points, we can get relate this to the graph. The linear line lastly has to be the directrix in which it entails equal distance between the focus and the vertex and that of the vertex and the linear line. This should be enough to determine the value of a. In this case, we can now get the expression of the parabolic function.