How to Graph a Parabolic Equation Without a Calculator?

Instead, we need to use the formula B2 - 4AC to determine the type of graph and its orientation. This formula is used to find the discriminant, which tells us whether the graph will have 0, 1, or 2 x-intercepts. In summary, to graph the given equation without a graphing calculator, we need to use the B2 - 4AC formula to determine the type of graph and its orientation. This will help us find the number of x-intercepts and plot the graph accordingly.
  • #1
Taiki_Kazuma
24
0
What's the process that needs to take place to be able to graph the following equation (not-using a graphing calculator):
x2 + 12xy + 36y2 + 2x - 3y - 9 = 0

I know to use the B2 - 4AC formula to identify the equation as being parabolic, though I don't understand the formula...

Looking at the equation at first, I thought you could factor it to resemble something like:
(x2 = y or y2 = x)

But, that's where my thinking ended (or maybe it never actually began...)


Thanks!
 
Mathematics news on Phys.org
  • #2
It's parabolic, but the axis of symmetry is not parallel to either the x or y axis,
 

What is a conic section?

A conic section is a curve created by the intersection of a plane and a cone. It can take the shape of a circle, ellipse, parabola, or hyperbola.

What is the general equation for a conic section?

The general equation for a conic section is: Ax² + Bxy + Cy² + Dx + Ey + F = 0. The values of A, B, and C determine the type of conic section, while D, E, and F determine its position and orientation.

How do you graph a conic section?

To graph a conic section, you will need to plot several points on a coordinate plane and connect them to form the curve. The type of conic section will determine the number of points needed and the shape of the curve.

What is the focus and directrix of a conic section?

The focus of a conic section is a fixed point that determines the shape of the curve. The directrix is a fixed line that is used to construct the curve. These two elements are important in determining the properties of a conic section.

Why are conic sections important in mathematics and science?

Conic sections have many real-life applications in fields such as physics, engineering, astronomy, and architecture. They also have connections to other mathematical concepts such as calculus and geometry, making them an important topic to study in mathematics.

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