We practiced plotting quadratic functions in standard form with f(x) = ax2 where a>1 or 0<a<1. We learned to identify key features of the graphs of quadratic functions written in vertex form. We learned to graph functions in standard form and show intercepts, maxima, and minima. Then we learned to determine how the values of a, b, and c affect the graph of f(x) = ax2 + bx + c. Next, we compared the properties of quadratic functions presented in different forms (algebraically, in a table, and graphically).

Key Features of a Quadratic Function – We learned to identify key features of the quadratic function using graphs, tables, and equations. Then we learned the effect of the value of a on the quadratic parent function. We learned that a quadratic function is a polynomial function in one or more variables in which the highest degree term is of the 2nd degree. The graph is a parabola. The value of the leading coefficient determines both the width of the parabola and the direction the parabola opens (upward or downward). We reviewed the attributes of a quadratic function such as minimum/maximum value and symmetry. Then we learned how the attributes affect the shape of a parabola.

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 completed several factoring trinomial problems to understand when to use negative and positive constant values. We checked our factoring of quadratics by multiplying the two binomial factors whose product is equal to the trinomial.

Adding and Subtracting Polynomials – We learned that a polynomial is a monomial or the sum or differences of two or more monomials. Polynomials can be added or subtracted by combining like terms. Polynomials are closed under addition or subtraction similar to integers. We practiced identifying the degree and number of terms of a polynomial. Then we practiced writing a polynomial in standard form. Next we practiced adding and subtracting two polynomials.

Exponential Growth and Decay – 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 solved equations with rational exponents using the properties of exponents. We reviewed the Power of a Power, Power of the Product, Product of Powers, and Quotient of Powers Properties. We learned that an exponential function models the relationship between two quantities that differ by a constant ratio. Exponential functions are modeled using f(x) = abx where a - is the initial amount and b is the constant ratio.

We practiced writing equations in standard form and slope intercept form. We reviewed how to find the slope and y-intercept. Then we reviewed how the slopes compare in parallel lines and perpendicular lines.

Standard Form – We learned to write and graph linear equations in standard form. We discovered that the standard form of a linear equation is helpful for identifying the x- and y-intercepts. These are used to graph the line and aid in understanding the constraints within a real-world context.
Parallel and Perpendicular lines – We learned to write equations to represent lines that are parallel and perpendicular to a given line. We graphed lines to show an understanding of the relationship between the slopes of parallel and perpendicular lines. Then we solved real-world problems that involve parallel and perpendicular lines.

2-1 Slope-Intercept Form – We learned how to write linear equations in two variables using slope-intercept form to represent the relationship between two quantities. Then we interpreted the slope and the intercept of a linear model. We practiced solving linear equations in the slope-intercept form, y = mx + b, where m is the slope, and the line intersects the y-axis at (0, b), so the y-intercept is b. We learned how to identify a positive or negative slope from the slant of the line. Then we identified graphs of zero and undefined slopes. Next, we reviewed the formula to find the slope when you have 2 points. We practiced finding slopes with the slope formula. Next, we practiced finding the slope from a graph. We practiced word problems where the point-slope formula helped us find the answer.