How can I deal with claims of technical difficulties for an online exam? So, on that assumption, we can find the tangent at the point $$\displaystyle (x_1, kx_1^2)$$, and then compare it to one of these equations. Founded in 2005, Math Help Forum is dedicated to free math help and math discussions, and our math community welcomes students, teachers, educators, professors, mathematicians, engineers, and scientists.

If they do, just replace the corresponding x in the y=m x + b equation to get the y coordinate for the intersection. Forums. 2x - k = 3x^2 + 2kx + 5. 3.

Stack Overflow for Teams is a private, secure spot for you and Parabola and Line Intersection Points. so the line and the parabola don't intersect iff the above quadratic equation has no real solutions, and this happens iff its discriminant is negative, so it must be: $$\Delta=(2k-2)^2-4\cdot3\cdot(5+k)<0\iff4k^2-20k-56<0\iff$$. To learn more, see our tips on writing great answers. I think whatever k is, it must be less than the y value of the Quadratic’s turning point, but I’m not sure how to proceed from there. Now turn that into a single quadratic and solve. .

In this video you are shown how to find the intersection between a straight line and a parabola using simultaneous equations. Dec 2007 59 0.

What was the most critical supporting software for COBOL on IBM mainframes? y(x) = m x + b (Eq 2), The two possible solutions (+ and -) for x are, You should check if your segment endpoints (in x) contains any of these two points.

Equation 3 are just the two possible solutions for this quadratic. Take the equation for the curve and put your line into y = mx +b form. $y=3x^2+2kx+5$. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. How often are encounters with bears/mountain lions/etc? By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy.

That gives you: A x2+ (B-m) x + (C-b) = 0 How many lithium-ion batteries does a M1 MacBook Air (2020) have?

What is the benefit of having FIPS hardware-level encryption on a drive when you can use Veracrypt instead? Why is Soulknife's second attack not Two-Weapon Fighting? $$Like this: This is the equation of the tangent to the parabola at any general point, $$\displaystyle \color{red}(x_1, kx_1^2)$$. I have an equation for a parabolic curve intersecting a specified point, in my case where the user clicked on a graph. 2y + x = 4. I am presented with these equations for a straight line and a parabola: Parabola equations and line through parabola equations. with the goal of calculating the range of values for k such that the line and parabola do not intersect. This will be helpful. Solution to Example 1. share | cite | improve this answer | follow | answered Sep 21 '19 at 19:41. so the line and the parabola don't intersect iff the above quadratic equation has no real solutions, and this happens iff its discriminant is negative, so it must be:$$\Delta=(2k-2)^2-4\cdot3\cdot(5+k)<0\iff4k^2-20k-56<0\iff Can you continue from here?

. I get the feeling there's a fairly straight forward way to do this, but I don't really know what to search for, nor am I very well versed in "proper" math, so actual code examples would be very much appreciated. Can it be justified that an economic contraction of 11.3% is "the largest fall for more than 300 years"? I would never have gotten this without your help.

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