## Week 10 – Midterm Review

This week i reviewed for the midterm.

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.

## Week 9 – Equivalent Forms of the Equation of a Quadratic Function

This week I learned the equivalent forms of the equation for a quadratic function.

Here is a common question:

This question asked me do each pair of equations represent the same quadratic function. I checked if they were the same by changing the equation in general form to standard form. To change the equation you need to factor by completing the square like we did in the last unit. The equations were then the same, so I knew they represented the same quadratic function.

## Week 8 – Transforming the graph

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

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

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

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.

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

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.

## Week 1 – Arithmetic Sequence

Find $t_{50}$ $t_{n}$ $s_{50}$ 5, 9, 13, 17, 21

$t_{n}=t_1+(n-1)d$

$t_{n}=5+(n-1)4$

$t_{n}=5+4n-4$

$t_{n}=1+4n$

$t_{50}=1+4(50)$

$t_{50}=201$

$S_n=\frac{n}{2}(t_1+t_n)$

$S_{50}=\frac{50}{2}(5+201)$

$S_{50}=25(5+201)$

$S_{50}=25(206)$

$S_{50}=5150$

This week I learned about sequences and I learned how to use these formulas properly. Now with any sequence I can find the different values.