Author: nickhershman

Thursday, 18 May 2017

Thursday, May 18

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In class: we studied the definition of /rational functions/ and looked at the graph of f(x) = 1/x and transformations of this parent function.

For example the function f(x) = 1/x

When transformed to g(x) = 3/(x-4) + 1 incurs a vertical stretch by factor 3 and horizontal shift of +4 to the right and vertical shift + 1. The asymptotes of the function are transformed with the function, so the asymptotes y = 0 and x = 0 of the parent function are vertically stretched (no effect) then vertically shifted (y -> 3fy + 1) and horizontally translated (x -> x + 4), so the x = 0 vertical asymptote moves right to x = 4.

Also, our nice point (1,1) moves 4 to the right and takes a vertical stretch by factor 3 followed by a vertical shift + 1, so (1 + 4, 1*3+1) = (5, 4)

Assignment: 9.6 on p. 536: 1-8, 10-12

Reminder: SBAC testing in Ms. Mac’s room tomorrow during 6th period.

Wednesday, 17 May 2017

Wednesday, May 17

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Assignment: 8.3 Task + RSG

These problems deal with proving congruence, perpendicularity, and parallelism using coordinate relationships. So for example, showing that the shape below is a rectangle by demonstrating that the slope of each pair of adjacent sides is perpendicular. We demonstrate perpendicularity by computing the slopes of the lines say slope(BC) = -(2/6) = -1/3 and the slope(AB) = 3/1 = 3. Since -1/3 and 3 are negative reciprocals we can see that sides AB and BC are perpendicular, and thus the angle at B is a right angle.

Tuesday, 16 May 2017

Tuesday, May 16

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In class we reviewed various forms of conics (ellipses, hyperbola, parabola) and learned about the general form of a quadratic

Ax^2 + bxy + Cy^2 + Dx + Ey + F = 0

Today's problems ask students to convert between this general form and the standard form of various other conic sections.

Assignment: 9.5 on p. 531: 1-8, 10, 13-16

Monday, 15 May 2017

Monday, May 15

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In class topic: ratios between similar figures. If a and b are the lengths of two corresponding dimensions between two similar figures, then we can say that all corresponding side lengths will be in the ratio

dfrac{a}{b}

Their area or surface area ratios will be

left(dfrac{a}{b}right)^2 = dfrac{a^2}{b^2}

Their volumes will be in the ratio

left(dfrac{a}{b}right)^3 = dfrac{a^3}{b^3}

Assignment: 11.5 on p. 595: 1-6, 10-17

Monday, May 15

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In class students worked through problems intended to help them create the distance formula

d^2 = (x_1 - x_2)^2 + (y_1 - y_2)^2

which becomes

d = sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}

They should understand how and why the formula works. And also see the relationship between the distance formula and the pythagorean theorem which it is based on

a triangle is right if and only if (its sides a​, b​ and c​) satisfy a^2 + b^2 = c^2

Assignment: 8.1 Task + RSG

Tuesday, 9 May 2017

, Tuesday, May 9

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In class: we worked through and discussed a practice SBAC test. Tomorrow students will be completing the Performance Task.

All 8th grade students are to bring their chromebook to class charged and ready for testing. No cell phones or internet device use allowed during testing sessions even if you are done.

Assignment: AGS students should be working to complete their Module 7 assessment which is still due at the start of class on Friday. So, at this point anything they have not completed should be completed at home. I would recommend completing problems 1 – 4 by tomorrow. And then completing #5 tomorrow evening.