Category: Math 11

Week 8 – Transforming the graph

anthonyv2015 on

This week I learned how to transform the graph of y=x^{2}.

Here is a common question:

This question asked me to graph without using a calculator or table of values. I graphed this by knowing that  x^{2} always creates a parabola and if the coffient of x^{2} is positive it faces up and if it is negative it faces down. Parabolas with a coffiecent of 1 have a congruent shape, with a pattern of 1, 3, 5 so i could plot the points. In the form of y=x^{2}+q q is the y intercept so that is where the vertex is. That information made it so I could graph without a calculator or table of values.

Week 7 – Interpreting the Discriminant

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This week I learned how to interpret the discriminant.

Here is a common question:

This question asked me to determine the values of k for which each equation has no real roots. The first thing you need to do is determine a formula for the discriminant which is the part of the equation in the quadratic formula under the radicand b^{2}-4ac<0. You make the formula to less than zero because you want the discriminant to be negative, you can’t take a root of a negative number so the equation will have no real roots. Then you substitute a b and c into to the and use BEDMAS to solve for k. You figure out if k is less than \frac{-27}{4} there will be no answer to the equation because the discriminant is negative.

Week 6 – Using Square Roots to Solve Quadratic Equations

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This week I learned how to solve quadratic equations using square roots.

Here is a common question:

This question asked me to solve the equation by completing the square. The first thing you need to do in this question is make it a square. You figure out the square by chopping the middle term in half \frac{5}{2} then square it \frac{25}{4}. You add \frac{25}{4} into the equation by making it a zero pair. Then you can solve for x by simplifying the part of the equation that is in brackets to (x+5/2)^{2} and add together the part not in brackets to get \frac{-37}{4}. After you have done this you move \frac{37}{4} to the other side of the equation and square root the whole thing. Then you can move \frac{5}{2} to the other side. Once you have done this you have simplified for x.

Week 5 – Solving Radical Equations

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This week I learned how to solve radical equations.

Here is a common question:

This question asked me if the equation had a real root. First I used algebra to solve for x. Then I determined what were the restrictions on x and when I did this I had to switch the more than or equal too sign to the other side because the coefficient was negative. After I just had to plug in -2 for x in the equation so I could check the answer. I determined this equation had a real root.

Week 4 – Adding and Subtracting Radical Expressions

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This week I learned how to add and subtract radical expressions.

This is a question I was stuck on:

In simplifying this problem you need to add together all the sides of the shape formed. When doing this you need to first simplify \sqrt{50} and then \sqrt{24}. Then you add the common radicands together to simplify the problem. I had trouble realizing that the roots were the values for the sides of the shape.

Week 2 – Geometric Sequences

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This week I learned about geometric sequences.

Here is a common question:

In solving this problem you first need to find “R” by using the formula \frac{t_2}{t_1}. Once you have found “R”, you can input all the values you have into the formula t_{n}=ar^{(n-1)}. Using BEDMAS go step by step to find your answer.