Today:

Warm-UpReview Quadratic Characteristics

Graphing Various Quadratic FunctionsClass Work

Warm- Up Exercises

The slope is 2,

which is positive

and the Y-intercept

is -2Therefore, the correct graph is

A

Warm- Up Exercises

The Y-intercept is:0

Write the equation for the line below:

The slope is:2

The equation of the line is: Y = 2x

Warm- Up Exercises3. Write the inequality for the graph below

The Y-intercept is:2

The slope is: -3The line is solid, not dotted. The equation is:

Y < -3x + 2

The following are all examples of quadratic equations: x2 = 25, 4y2 + 2y - 1 = 0, y2 + 6y = 0, x2 + 2x - 4 = 0

The standard form of a quadratic is written as: ax2 + bx + c = 0, where only a cannot = 0

A variable in a quadratic equation can have an exponent of 2, but no higher.

Quadratic Review

A. The graphs of quadratics are not straight lines, they are always in the shape of a Parabola.

Important points on a Parabola:

1.Axis of Symmetry:The axis of symmetry is the verticle or horizontal line which runs through the exact centerof the parabola.

Graphing Parabolas & Parabola Terminology

Important points on a Parabola:2. Vertex: The vertex is the highest point (the maximum), or the lowest point (the minimum) on a parabola.

Notice that the axis of symmetry always runs through the vertex.

Graphing Parabolas & Parabola Terminology

Graphing Various Types of Quadratic EquationsRemember, the standard form of a quadratic equation is: ax2 + bx + c = 0Since the solutions or roots to a standard equation are where the line crosses the x-axis, the y value is always zero. As such, we can substitute y for zero: y = ax2 + bx + cFinally, since the y variable is dependent on the x, or is a function of x, we can substitute the y for the function of x, or (f)x: (f)x = ax2 + bx + c

Regardless of which form is presented, the problem is solved in the same way.

In this lesson, you will graph quadratic functions where b = 0.

Graphing Various Types of Quadratic Equations

The first step is to make a table. We can use the following x values today:

Then complete the values for y and graph the parabola. This must be done for each graph completed today.

Graphing Various Types of Quadratic Equations

Graphing Various Types of Quadratic Equations

Using the same graph, graph y = - ¼x2. Compare this graph with the other two.

The first step is to make a table. We can use the following x values :

Graphing Various Types of Quadratic Equations

Graphing Various Types of Quadratic Equations

Graphing Various Types of Quadratic Equations

Class Work:

Girls, do odd problems; Guys even. Create tables for each problem.

One problem for each graph.

Finding the Axis of Symmetry and Vertex

1. Finding the Axis of Symmetry: The formula is: x = - b/2a Plug in and solve for y = x2 + 12x + 32We get - 12/2; = -6. The center of the parabola

crosses the x axis at -6. Since the axis of symmetry always runs through the vertex, the x coordinate for the vertex is -6 also.

There is one more point left to find and that is they-coordinate of the vertex. To find this, plug in the value of the x-coordinate back into the equation and find y. y = -62 + 12(-6) + 32. Y = 36 - 72 + 32; y = - 4 The bottom of the parabola is at -1 on the x axis, and - 4 on the y axis.

Finding the Axis of Symmetry and Vertex

y = x2 + 12x + 32