Algebra III Academic
Solving Quadratic Equations

Review graphing quadratic functions
Standard Form: ______________________________________
Parabola in Standard Form: Graph y = x2 – 6x + 2 and use the graph to complete 2-5.
1. Make an x,y chart (table of values) for each integer from x = -2 through x = 8. Plot these points on the
graph below.
2. The low point of the graph is called the vertex. Write the coordinates of the vertex.
3. The graph is symmetrical to a vertical line through the vertex. This line is called the axis of symmetry.
Draw a dotted line on your graph to represent the axis of symmetry.
4. What does the y-intercept equal? Where does this number appear in the original equation?
5. There are two x-intercepts. Approximately, what do they equal?
Vertex Form: ___________________________________________________________
Write the equation in Vertex form and then graph. y = x2 – 6x + 2
1. Make an x,y chart (table of values). Use the vertex to determine other integers that should be used in the
table.
1. The low point of the graph is called the vertex. Write the coordinates of the vertex.
2. The graph is symmetrical to a vertical line through the vertex. This line is called the axis of symmetry.
Draw a dotted line on your graph to represent the axis of symmetry.
3. What does the y-intercept equal? Where does this number appear in the original equation?
4. There are two x-intercepts. Approximately, what do they equal?
Example #3 : Transform y = -3x2 - 24x + 11 into vertex form and then do the following:
Make an x,y chart (table of values). Use the vertex to determine other integers that should be used in the table.
1. The low point of the graph is called the vertex. Write the coordinates of the vertex.
2. The graph is symmetrical to a vertical line through the vertex. This line is called the axis of symmetry.
Draw a dotted line on your graph to represent the axis of symmetry.
3. What does the y-intercept equal? Where does this number appear in the original equation?
4. There are two x-intercepts. Approximately, what do they equal?
Generalization:
-
If x2 term has a positive coefficient then _________________________
-
If x2 term ahs a negative coefficient then _________________________
Class work: Page 187, 32-42 Even
Homework: Page 187, 31-43 odd
32.
34.
36.
38.
40.
42.
31.
33.
33.
35.
37.
39.
41.
43.