Author: Jessica Brockway

Length of Lesson: 45 minutes

Class: Algebra 1

Source(s) of Lesson:

http://www.purplemath.com/modules/grphquad3.htm

TEKS addressed:

(A.1.E) interpret and make decisions, predictions, and critical judgments from functional relationships

(A.2.A) identify and sketch the general forms of linear (y = x) and quadratic (y = x2) parent functions

(A.9.B) investigate, describe, and predict the effects of changes in a on the graph of y = ax^2 + c

(A.9.C) investigate, describe, and predict the effects of changes in c on the graph of y = ax^2 + c

Learner Outcomes: Students will learn the different parts of the quadratic equation and how they effect the graph of it.

Supplementary materials:

Graphing calculators

Projector for graphing calculator

Attached worksheet

TEACHER DOES	STUDENT DOES
ENGAGEMENT/EXPLORATION
Have students plug in various graphs with just a changed y= -10x^2+5 y=1x^2+5 y=.0001x^2+5 y=100x^2+5 - what happens? Have students plug in various graphs with just c changed y=1x^2+0 y=1x^2+5 y=1x^2-10 y=1x^2+.5 - what happens?	Students plug the equations into their graphing calculators and compare
EXPLANATION
a is often called the leading coefficent it determines how “skinny” or “fat” the parabola is when a is large is the parabola skinny or fat? What about when a is small? Now what is a when the parabola is “smiling”? What is a when the parabola is “frowning”? Now what does c do to the graph? Correct. It is the y intercept. So when c is negative where the y-intercept on the graph? And when it is positive?	Skinny!! FAT!! Wide!! Positive Negative Moves the graph up and down Where the point (vertex is on the y axis) It is in the negative y’s In the positive y’s
EVALUTION
Give students attached worksheet	Students complete worksheet (finish for homework if necessary)
ELABORATION
What are the points called where the parabola crosses the x-axis? Does the equation just give you those numbers? (have students trace them on their calculator to get coordinates)	X intercepts No. how do we get them?

WORKSHEET:

How would the graph of the function y = x^2 + 4 be affected if the function were changed to y = x^2 + 1?

F) The graph would shift 3 units up.

G) The graph would shift 3 units down.

H) The graph would shift 3 units to the right.

J) The graph would shift 3 units to the left.

In the graph of the function y = x^2 + 5, which describes the shift in the vertex of the parabola if, in the function, 5 is changed to −2?

A) 3 units up

B) 7 units up

C) 3 units down

D) 7 units down

When graphed, which function would appear to be shifted 2 units up from the graph of f(x) = x^2 + 1?

F) g(x) = x 2 − 1

G) g(x) = x 2 + 3

H) g(x) = x 2 − 2

J) g(x) = x 2 + 2