Quadratics B

In this second part of the Quadratics unit, we will look at a couple of things.
Writing and graphing equations in vertex form.
Identifying the transformations of a quadratic
Use of quadratics in figuring projectile motion
Comparing different quadratic models
and
Looking at nonlinear systems of equations and inequalities.

The first thing we will look at is rewriting from standard form to vertex form. We will also look at rewriting from vertex form to standard form but we don't use that particular operation often. It is a good activity to help see the relation ship between the two forms.
Below is a short video to help explain the process in case you have any questions about what we covered in class.

Below is a written step by step "how to" for rewriting into vertex form with an example.

Below is the Vertex Form Homework.

Equations of Circles and Graphing Circles

Circles are not exactly quadratic but do have several things in common. They are both 2nd power polynomials and can be simplified and graph when in the proper form.
Standard form of a circle is;
(x - h) squared + (y - k) squared = r squared where (h, k) is the center of the circle and r is the radius.
In order to graph, simply plot the center point, count right, up, left, and down from the center the number of squares equal to the radius and sketch the circle as best you can.

Quadratic Inequalities

We are now going to take a look at quadratic inequalities. As we (hopefully) know, inequalities identify an area of the coordinate plane that satisfy a given inequality. It shows the area where a function is greater than, greater than or equal to, less than, or less than or equal to a certain value.
These type problems result in an infinite number of solutions identified by a shaded region of the coordinate plane.

The homework for this section is below.

The last section in Quadratics B is solving non-linear systems of equations, that is, systems of either two quadratic functions or a quadratic and a linear function. We can solve these either algebraically using substitution or graphically. Both methods work well and will be utilized in the homework exercises.

When solving algebraically, be sure and show all steps. If the solution is a radical, simplify the radical. When solving graphically, if the solution is not an integer, round to the nearest hundredth.

When graphing, you don't need to list a table of values but make sure a minimum of 5 point are plotted including the vertex and two points on either side of the vertex.

Identify the solutions of these systems as ordered pairs (since that's what they are.)

Quadratics B Test Review
Do # 1-24

Test Review Answers