## Week 15 – Multiplying Rational Expressions

This week I learned how to multiply rational expressions.

Here is a common question:

This question asked me to simplify the expression. The first thing i did in this question was reduce the coefficients, and then I combined the two expressions together since it was multiplying. After I factored out what I could from the expression to figure out which factors can cancel out. Then i just reduced a to figure out my answer. The last step was to find out the non-permissible for a, and this means the values that will not make the denominator equal to zero. This is because in a division question you aren’t allowed to have the denominator  equal to zero.

## Week 14 – Graphing Reciprocals of Quadratic Functions

This week I learned how to graph quadratic reciprocal functions.

Here is a common question:

This question asked me to figure out the parent function of the graph. I knew it was c, because I drew the parent graph by going through the invariant points. I also knew that the graph only had one root, because there was only two hyperbolas. Then I used 1,3,5 to draw the rest of the graph.

## Week 13 – Graphing Reciprocal Linear Functions

This week I learned how to graph linear reciprocal functions.

Here is a common question:

This question asked me for each pair of functions, use the graph of the linear function to sketch a graph of the reciprocal function, and state the domain and range. First I sketched y = x + 2 by using the slope and the y intercept. Then i had to sketch the reciprocal of that function. First I figured out where the invariant points so I could draw the vertical and horizontal asymptotes. The graph never cross the asymptotes. Then I could sketch in the reciprocal of the graph. The domain and range are both elements of the real numbers, but they do not go through the origin of the graph, because there is no reciprocal for 0.

## Week 11 – Graphing Quadratic Inequalities in Two Variables

This week I learned how to graph quadratic inequalities with two variables.

Here is a common question:

This question asked me to graph the inequality $y<-x^{2}+8$ and state 3 points that satisfy the inequality. I graphed this inequality by using a to know that the graph opens down and is in the form 1,3,5 and 8 is the y intercept. I tried those three points and they satisfied the equation so I knew to shade in the inside on the graph. I, also knew that it was a dotted line because the inequality is less than < and not less than or equal too.

## 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.