Day: November 6, 2017

Week 9- Pre Calc 11

katelynw2015

This week we did lots of review, but we also learned a new lesson on Modelling using quadratic equations. ThIs is the lesson that I struggled with the most in the unit and it’s easier to explain using pictures and numbers rather than words.

 

In the example we know that when x and y are added together they need to equal 24 so we made the equations x+y=24. The equation can also be represented by y=x-24. On the right side of the page we graphed out the equation to show us a visual representation of our equation. On the graph we made x=0 so we need to do the same to the written equation,

x(x-24)=y

0(0-24)=y

0+24/2=12

This means that

f_12=12(24-12)

=12(12)

=144

 

 

 

Week 8- Pre Calc 11

katelynw2015

For week 8 in Pre-calc 11 we learned to analize Standard form (vertex form). In my opinion this is the easiest form to graph becasue you are already given the vertexand with it you can find the x and y intercepts, the line of symmetry, and the domain and range. Each number in the standard form tells you something different about how it needs to be graphed.

Standard form: y=a(x-p)^2+q

a- determins the width of the graph. If a<1 then the graph will become wider and if a>1 then the graph will become thinner. A also determines if the graph will be opening up or down. If a is positive then the graph will open up, but if it is negative then it will open down.

p- determins the horizontal translation of the graph. If p is positive then the graph will slide left to the negative side. If p is negative then the graph will slide right to the postivive side. Basically you do the opposite of what p really is, so if you have p=-2 then you go +2 along the x axis.

q- determins the vertical translation of the graph. If q is negative then you slide the graph down the y axis into the negative side. If q is a positive then you slide the graph up the y axis into the positive side

This form is also known as vertex form because it gives you the vertex, which will we (p,q)

Example: y=3(x-2)^2+1

Just by looking at this I can tell that the graph is going to be skinnier, move 2 to the left (positive) and will also go up one along the y-axis.

There is no x-intercepts because y>1 and the graph is opening up which means the graph will not touch the x-axis

Week 7- Pre Calc 11

katelynw2015

In week 7 we started looking over properties of a quadratic function. In this lesson we determined the characteristics of a quadratic function and how to solve it.

We determined if a table of values represented a quadratic function. You could tell this by seeing how much y went up.

Example: 5,0,-7,-16,-27

to get from 5-0 you -5, to get from 0–7 you -7, and to get from -7–16 you -9. The pattern here is you are adding 2 to how much you subtract each time

A few of the first things I learned include; finding the vertex, the x and y intercepts, the line of symmetry, and the domain and range.

Example: 2x^2+8x+6

Vertex: (-2,2)

x-intercepts: (-3,-1)

y-intercept: (6)

Line of symmetry (-2)

Domain: (XER)

Range: (y>-2)