We learned that an exponential growth function increases by a fixed percent and an exponential decay function decreases by a fixed percent over each interval. We learned to construct exponential growth and decay functions given a description of a relationship. Then we recognized if a situation can be modeled with exponential growth or decay, and interpreted the parameters of the model in context. Next we became familiar with the terms compound interest, exponential growth, and growth factor.
We learned to graph functions in standard form and show intercepts, maxima, and minima. We compared the properties of quadratic functions presented in different forms (algebraically, in a table, graphically).
We learned to compare properties of quadratic functions. We found the x-coordinate of the vertex by using the formula –b/2a. Next, we plugged the x-coordinate into the original equation to find the y-value. Then we applied these principles to real-world problems.
We reviewed the attributes of a quadratic function and learned how the attributes affect the shape of a parabola. We practiced plotting quadratic functions with f(x) = ax2 where a<0, a>0, a>1, and 0<a<1. We learned to identify key features of the graph of quadratic functions written in vertex form. Then we practiced graphing quadratic functions in vertex form.
Factoring Special Cases – We learned that when a trinomial has the pattern a2 + 2ab + b2, then it can be factored as (a + b)2. If a2 - 2ab + b2 then (a - b)2. If a binomial has a pattern a2 - b2, then it can be factored as (a + b) (a - b) where the middle term equals 0 or cancels out. We practiced identifying and factoring a trinomial that is a perfect square or a binomial that is a difference of two squares. Then we factored special cases of polynomials within the context of real-world problems. We worked on learning and using the quadratic function.
Factoring – We learned that the greatest common factor of the terms of a polynomial is the greatest common factor of the coefficients and the variable or variables, using the number of instances of the variable that are common to each term. We learned that when a trinomial is in the form x2 + bx + c, the factors are found by identifying a pair of integer factors of c that have a sum of b and then using the factors to write binomials that have a product equal to the trinomial.
We continued to practice finding the solutions to an absolute value equation. Then we practiced finding the greatest common factor of polynomials and factoring it out to simplify the equation.
We worked on solving absolute value algebraic equations. We went over the fact that
to solve absolute value equations, we isolate the absolute value expression, then split it into two separate equations: one where the expression equals the positive number on the other side, and another where it equals the negative. Then we solved both equations. Then we went over transformations of the absolute value function.
We worked on understanding fractions for exponents and converting between radicals and exponents. We worked on multiplying powers and finding the power of a power. We reviewed the three equations of a line.
We worked on extra credit packet. We decided to start with finding the equation of a line given the slope and y-intercept. Then we practiced finding the equation of a line given a table of values or a point and the slope. We also practiced finding the equation of a line from a graph.
