Identifying Quadratic Equations and Circles

The Standard Form of a Circle: (x-h)^2+(y-k)^2=r^2

The Standard Form of a Quadratic Equation: ax^2+bx+cy^2+dy=e

To find out whether an equation is a Circle, Hyperbola, Ellipse, or a Parabola use the equation: Ax^2+Cy^2=E.

If A=C, the equation is a CIRCLE.
If A does NOT equal C and has the same sign, the equation is an ELLIPSE.
If A=C, but has different signs, the equation is a HYPERBOLA.
If A or C are 0, the equation is a PARABOLA.

Can you multiply these matrices?

In order to know if you can multiply a couple matrices , the number of columns in the first matrix must equal the number of rows in the second matrix. So yes , you can multiply these matrices.



You can multiply these matrices too . The number of columns in matrix one equal the number of rows in the second.

Dimensions of a Matrix

3x3 : 3 rows and 3 columns

3x2 : 3 rows and 2 columns

3x3 : 3 rows and 3 columns

1x3 : 1 row and 3 columns

To figure out the dimensions in a matrix , go by Row x Column . The number of horizontal rows x the number of vertical columns.

Systems of Equations

In Graph 3, the system of equation is an Inconsistent equation . It's lines are parallel and parallel lines will never cross , so there could never be a solution. Inconsistent and No Solution.

In Graphs 1 and 4, two lines are crossing at one point , therefore it only has one solution . This system of equation will be called Independent and Consistent.

In Graph 2, the line looks to be one line , but it is actually two lines drawn together. These two lines intersect at every point along their length. This System of Equation would be called Dependent , and the solution would be the whole line.

The graphing of the inequality in number 20 is correct , but the line should be dotted , not solid. The graphing in number 21 is also correct , but the shaded should be below the graph.

In the first inequality y<x+3 , the graphing is correct , but the line should be dotted because the problem is less than.  In the second inequality , the graphing is correct also , but should be shaded above the line.

 (1,2) is a solution for the system 5x-y=7, but it is not a solution for the other system x+4y= -5.