Month: November 2018

Week 12/ Absolute value functions

kaidenh2016 on

Absolute value functions

I’ll be graphing a absolute value equation, graphing it, and showing it in piecewise notation.

y= |-3x+9|  <——- Note: absolute value brackets (|x|)

With a normal line, (-3x+9) it would go below the x-axis, but when there are absolute value lines in the equation it makes it so the line does not go into the negitive not. Which also means it does not go below the x-axis, istead it just rickashays off and comes right back up. It refects the original line and bounces off the x-axis.

 

Now that we haved graphed we must state it peace wise notation. The point that intercecpts with the x axis is where you will be basing the x is < or > off of. For stating the x is < or > is with two equations, becuase the graph shows two line reflecting off the x axis there are two equations. 1. -3x+9 and -(-3x+9) then you state whether  x is < or > for the number on the x axis.

y = {-3x+9  if x < and equal to 3}

y = {-(-3x+9)  if x > 3}

To figure out if x is < or > you must test a point on the x axis to see if its true. Test numbers before and after three.

Week 11/ Solving system of equations graphically

kaidenh2016 on

Solving system of equations

First you must be able to show the equation graphically. By doing so you have to show any linear equations into y=mx+b form; then change any quadratic equations into factored form or vertex form.  After you have algebraically changed all the equations you can then graph the equations and see where they intercept. Then that will be your solution.

There can be three type of solutions when solving for x equations that are linear and quadratic. The first one is no solution, the second is one solution, and the third is two solutions.

Equations: y= 2x^2 + 4x + 4

y= -2x+7

The graph states that there is no solution because the equation does not touch or intercept with each other.

Week 7 blog post/ Discriminant

kaidenh2016 on

Discriminant is used when figuring out how many solutions and if they are real roots. The Discriminant is b^2 – 4ac$, which looks familiar beucase it is the discriminant of the equation in the quadratic formula. Just by the simple equation b^2 – 4ac$ it can tell us alot about the quadratic equation before we even start solving.

If you get zero means x is one solution one solution, if the x is greater than zero you have two solutionsand you know it will be rational, if you get less than zero there is no solution.

Week 10 blog post/ Solving Quadratic Inequalities

kaidenh2016 on

In Solving Quadratic Inequalities, you need to know three steps.

Step 1: Factor the exspression

Step 2: Determine the zeros

Step 3: Use a sign chart for each factor to the left and right of zeros

Note: Test numbers a number on all the opposing sides of the x intercepts

(Key things to know when solving Quadratic Inequalities is to make sure the the statement is always true, if its not you know your answer is wrong or there is no possibility.)

Week9/solving A with factored form

kaidenh2016 on

Question: A graph passes through B(2,-5) and has x-intercepts -3 and 4

Before solving its good to analyse the question first. Passes through B(2,-5) represents x and y, well x intercepts represents the x intercepts. An equation that can use both of these clues is factored form since factored form has the x-intercepts in the equation.

Factored Form y= a(x-x1) (x-x2)

When plugging in the x intercepts from the equation you get  y= a(x+3) (x-4), this question may look solvable but it has more than one variables so you cannot solve it yet for A. Thats why you put the x and y into the equation. Now your left with -5= a(2+3) (2-4). From there you can now solve for a. (EXAMPLE BELOW)Now the equation is y= \frac{1}{2}(x+3) (x-4) now it is a complete equation and can be changed and graphed.