April 2019 archive
This week was a shortened week so we didn’t go over as much stuff as the previous weeks.
We learned how to graph quadratic and linear inequalities in one variable and two variables.
To graph a quadratic inequality you need to find the y- intercept and the vertex and use the clues given to graph it and find possible solutions and where to shade in the graph.
the y intercept is -18
you can tell it opens up because the x^2 is positive
the vertex moved
and the pattern is 1.3.5 because the leading coefficient is 1
So then you would factor
and with those you can find your vertex from -8 and +2 being your x- intercepts
to find the vertex you would do -8+2/2
so your vertex is -3
and by plugging it back into you equation you can find the minimum point connected to the vertex and graph it
we know that its a doted line because the > doesn’t have a line underneath it
and we can put a test point into the original equation to know if its shaded in, in the certain area.
We did review for most of the week so this is one of the things i reviewed today. so i revisited the idea of factoring polynomial expressions like we learned last year in grade 10, and like we learned in the previous units.
For example, when we started the practicing of factoring expressions I remembered that for the second number in the trinomial (abc: letter B) it was the sum of adding the two numbers together and the third number in the trinomial (abc: letter C) was the sum of the two numbers multiplied.
x2 + 7x + 10
I could go through the list of factors if 10 and then find 2 that add together to get the sum of 7.
you notice that 2+5 equals 10 so then you input those into the expression
(x + 2) (x + 5)
This week we continued to go over quadratic functions.
I learned that you could model problems with quadratic equations,
for example: Find two integers with a sum of 24 and the greatest possible product.
product is a multiplication word so we know that we have to multiply it to find it meaning that the PRODUCT= x ∙ y
we have to re-arrange the equation that we already have so that we can get it to have only one variable.
product=x ∙ (24-x)
(zero product law)
x=0 (1st term)
x=24 (inside brackets)
LOS= 0+24 divided by 2
then we would insert that into our standard form
p(x)= x (24-x)
p(12)= 12 (24-12)
144 is our maximum product
I found it very interesting that we didn’t need to have a word problem that involves something being thrown or going up nd down like a U shape and that instead we could still help solve it and graph it like one.
This week was a tough week coming back from spring break and my most struggle this week was trying to stay in focus the whole class since we had two weeks off I definitely missed a lot this week because I couldn’t keep in focus, we learned how to graph quadratic equations,
we learned that the vertex is the exact midpoint of the x- intercepts.
the standard form is ax² + bx + c = 0
So for a function to be quadratic it has to have x2 in it, so that it will graph a parabola that will make a U shape on the graph.
The parent function or where all parabolas start is From this form y=x2
we can change the equation so that we can add variables to show if the parabola will be moved up or down, side to side, which way it faces and how skinny or thick it will be.
this means the parabola will be 5 up on the y-axis but zero on the x-axis.
7 key characteristics: Vertex (most important), Domain, Range, Maximum/Minimum, x-intercept, y-intercept, and the line of symmetry.