New Unit!

We started a new unit today. Unit 5 has us going back to algebra concepts so we will review concepts from the fall and build on them.

Today's concept is graphing quadratic equations given in standard form, y = ax² + bx + c. Much of this lesson is review. However, one part of the lesson is new:

• To find the vertex of a parabola, first find -b/2a. This value equals x for the vertex. Then, plug this value into the equation and solve for y. These values locate the vertex.

Once the vertex has been located, use a table or chart to organize your work picking values for x, substituting them in, and solving for y. Plot these points to find the shape of the parabola.

Along with graphing the quadratic equation, we expect students to be able to answer the following questions:

• Opens: the graph opens up when a > 0 and the graph opens down when a < 0 ;
• Vertex: the point found using the directions above;
• Min/Max: the vertex is a minimum when the graph opens up and the vertex is a maximum when the graph opens down;
• AOS: the axis of symmetry is the line "x = (-b/2a)";
• X-intercepts: the points where the graph crosses the x-axis. This can be none, one, or two points. When the graph crosses between two integers, simply state "between (m, 0) and (n, 0)" where m and n are the integers;
• Domain: the domain is the set of all possible x that can be used in the equation. For the quadratic functions it is {all real numbers};
• Range: the range of a quadratic function is based on the vertex and whether it is a maximum or a minimum. When the vertex is at the top of the graph (maximum), then the range is {y ≥ the y-value in the vertex}. When the vertex is at the bottom of the graph (minimum), then the range is {y ≤ the y-value in the vertex};
• End Behavior: the arrows at the ends of the graph of a quadratic function either both point up (going toward positive infinity or +∞) or both point down (going toward negative infinity or -∞);
• Intervals of Increasing and Decreasing: the intervals are determined by where your pencil draws downward (decreasing) and where it draws upward (increasing) when making the parabola. If the interval is to the left of the AOS, then write {x < the x-value in the vertex}. If the interval is to the right of the AOD, then write {x > the x-value int the vertex}.

Homework: Page 107, #24 - 30 even; Page 109, #16 - 26 even. For all graphs, also include x-intercepts, domain, range, end behavior, and intervals of increasing and decreasing.

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