1
vote
2answers
764 views

coefficients of quadratic function?

In a quadratic function: coefficient $a$ controls the speed of increase/decrease from the vertex. coefficient $b$ controls the downward slope as the function crosses the y-axis. I don't really ...
3
votes
3answers
140 views

Is it possible to find out $x^2$ parabola and function from 3 given points?

I am programming a ball falling down from a cliff and bouncing back. The physics can be ignored and I want to use a simple $y = ax^2$ parabola to draw the falling ball. I have given two points, the ...
2
votes
0answers
133 views

My solution is right and the book is wrong (parabolas) or did I misunderstand it?

Find the equation of the parabola with the vertex at the origin; directrix 2x = 3 So what I did is, find the equation of the directrix $$x = \frac{3}{2}$$ and then because its the directrix, the ...
0
votes
2answers
375 views

Plotting quadratic equation in two variables

I need to draw a conic curve when quadratic equation in two variables is given: $$Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0$$ Since I can't simply check whether the pixel is solving the equation, what I'm ...
3
votes
2answers
157 views

Integer points in a curve?

The question asks for necessary and sufficient conditions for a given curve to have integer points, that is, $(x_k,y_k)$ such that $x_k,y_k\in\mathbb{Z}$. For example, a necessary and sufficient ...
1
vote
0answers
147 views

Math function for parabola

I need an implicit function that plots the parabola that I am showing you in the picture. Everything you need is shown there. The radius of the thickness of the parabola must be 3. Thank you in ...
2
votes
3answers
271 views

Find the smallest $k\in \mathbb{Z}$ such that $f(x)=x^2-3x+k$ and $g(x)=x-2$ do not intersect.

$$ \large{ \text{Here are some instructions from the original question: } \ \\ } $$ $$ \large{ k \in \mathbb{Z} \ \ \land \\ f(x)=x^{2}-3x+k \ \ \land \ \ g(x)=x-2 \ \\ \text{And, there is NO any ...
6
votes
3answers
1k views

Are there parabolic and elliptical functions analogous to the circular and hyperbolic functions sin(h),cos(h), and tan(h)?

In matters of conic sections, are there other properties such that it helps to group the circle and hyperbola in one, and the parabola and ellipse in the other?
4
votes
3answers
191 views

What is the most direct way to derive an equation for a parabola from its x and y intercepts?

I have a pair of points at my disposal. One of these points represents the parabola's maximum y-value, which always occurs at x=0. I also have a point which represents the parabola's x-intercept(s). ...