Solving equations algebraically

9= -1(-2x+6)

9=2x-6

15=2x

x=7.5

Simplify 5/a+3/a

=8/a

1. Find common denominator (multiply denominator to do so)
2. add or subtract across like normal.

Simplify 4/a-2/3

12-2a/3a

An asymptote is a line that identifies the boundaries of a curve. As of pre caluclus 11, the y asymptote (horizontal)=0. The x asymptote (vertical) is a little bit more complicated. Looking at the y axis, identify where the point of line is at -1 and 1. In between these points is where the x asymptote will be.

Today we reviewed some key points on absolute values:

-The values are ALWAYS positive.

-When graphing, the linear or quadratic equation will never enter the negative area (y.) As shown below, the line reaches 0 on the y axis and reflects up.

This week, we learned how to read a linear equation.

y=2x-1

In this equation, the form is y=mx+b. The b in this situation is -1. This represents the y intercept. The mx in this situation is 2x. This represents the slope. The slope is 2/1 (2 right, 1 up.)

This week we worked on converting from standard for to vertex form by completing the square.

Ex: y=x²+4x-5

y= (x²+4x+4)-5-4

y=(x+2)²-9

This week, we focused on analyzing quadratic functions and changing them to parabola’s.

Identifying the y intercept of the graph of a quadratic function.

y= 3-14x+5x²

y= 3-14(0)+5(0)²

y=3-0+0

y=3

The discriminant is a number that shows if the value of x is rational/irrational/how many roots it has.

The formula we use to find the discriminant of a quadratic equation is b²-4ac

ex: 2x²-10x+3=0

The first step is to identify the values of a,b and c:

a=2

b=-10

c=3

We will then plug these numbers into the formula:

-10²-4(2)(3)

100-24

=76

The discriminant for 2x²-10x+3=0 is 76. This means that this quadratic equation has 2 irrational roots. This is because the equation is positive yet not a perfect square.