1. Today:
Warm-Up
Review Quadratic Characteristics
Graphing Various Quadratic Functions
Class Work
2. Warm- Up Exercises
The slope is 2,
which is
positive
and the Y-
intercept
is -2
Therefore,
the
correct
graph is
A
3. Warm- Up Exercises
Write the equation for the line below:
The Y-intercept is: 0
The slope is: 2
The equation of the line is:
Y = 2x
4. Warm- Up Exercises
3. Write the inequality for the graph below
The Y-intercept is: 2
The slope is: -3
The line is solid,
not dotted. The
equation is:
Y < -3x + 2
5. Quadratic Review
A variable in a quadratic equation can have an exponent
of 2, but no higher.
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. The graphs of
quadratics are not straight
lines, they are always in
the shape of a Parabola.
6. Graphing Parabolas & Parabola Terminology
Important points on a Parabola:
1.Axis of Symmetry:The axis of symmetry is the verticle
or horizontal line which runs through the exact center
of the parabola.
7. 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.
8. Graphing Various Types of Quadratic Equations
Remember, the standard form of a quadratic equation is:
ax2 + bx + c = 0
Since 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 + c
Finally, 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.
9. Graphing Various Types of Quadratic Equations
In this lesson, you will graph quadratic functions where b = 0.
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.
11. 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 :
15. Class Work:
Girls, do odd problems; Guys even.
Create tables for each problem.
One problem for each graph.
16. 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 + 32
We 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.
17. Finding the Axis of Symmetry and Vertex
y = x2 + 12x + 32
There is one more point left to find and that is the
y-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.
