Lesson 1: 3-1 Graphing Quadratic Functions

What strategies might you use to avoid making an error with a negative sign?
How could spacing out your work more help eliminate possible errors?

quadratic function
quadratic term
linear term
constant term
parabola
axis of symmetry
vertex
maximum value
minimum value

A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.
A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

SAT questions related to solving quadratics: 2-3-13,3-3-14,1-3-16,5-3-3,8-3-16,1-4-25; analyzing graphs: 3-4-12,8-3-11,8-4-19,6-3-11

Graphs of quadratic functions of the form f(x)=ax^2+bx+c, where a does not equal zero, are called parabolas. All parabolas have an axis of symmetry, a vertex, and a y-intercept. Some parabolas open up, and others open down.

Eddie is organizing a charity tournament. He plans to charge a $20 entry fee for each of the 80 players. He recently decided to raise the entry fee by $5, and 5 fewer players entered with the increase. He used this information to determine how many fee increases will maximize the money raised.

Make sure students realize that f(x) and y can be used interchangeably, and also that the maximum or minimum value of the function is given by the y-coordinate of the vertex of the parabola.

If students struggle to solve real-world problems involving maximum or minimum values, then encourage students to explain to partners their plans for solving. Suggest that the listening partner take notes about their speaking partner's strategies, asking questions as needed for clarification.

McGraw Hill resources

McGraw Hill resources