3.2 Graphing Quadratic Functions The equation of a quadratic - - PDF document

MPM2D1 ­ U3L2 ­ Graphing Quadratic Functions 1

3.2 Graphing Quadratic Functions

The equation of a quadratic relation may be written in several forms: Factored Form: Standard Form: Vertex Form: Last class, we looked at graphing equations in Vertex Form. Today, we will look at graphing equations in the other 2 forms.

MPM2D1 ­ U3L2 ­ Graphing Quadratic Functions 2

• Ex. 1 Graph x2 ­ 8x + 12

Graphing by Factoring

• 1. Find the x­intercepts of the parabola.
• 2. Plot the x­intercepts.
• 3. State the equation of the axis of symmetry.
• 4. Find the y­coordinate of the vertex.
• 5. Draw a smooth curve through the three points you know to be on the parabola.

MPM2D1 ­ U3L2 ­ Graphing Quadratic Functions 3

• Ex. 2 Graph x2 + 4x

Graphing by Factoring

• 1. Find the x­intercepts of the parabola.
• 2. Plot the x­intercepts.
• 3. State the equation of the axis of symmetry.
• 4. Find the y­coordinate of the vertex.
• 5. Draw a smooth curve through the three points you know to be on the parabola.

MPM2D1 ­ U3L2 ­ Graphing Quadratic Functions 4

• Ex. 3 Graph ­2x2 + 8x ­ 5

Graphing by Partial Factoring

• 1. Factor the leading coefficient and x from the first two terms.
• 2. Find the two values of x that make the factored part equal to zero.
• 3. Plot the coordinates of the two points you found.
• 4. State the equation of the axis of symmetry.
• 5. Find the y­coordinate of the vertex.
• 6. Draw a smooth curve through the three points you know to be on the parabola.

MPM2D1 ­ U3L2 ­ Graphing Quadratic Functions 5

• Ex. 4 Graph 2x2 + 6x + 1

Graphing by Completing the Square

• 1. Factor out the leading coefficient from the first two terms

.

• 2. Divide the coefficient of the x term by 2 and then square it; add and subtract this

number after the x term.

• 3. Remove the negative number from (2) from the brackets by

multiplying it by the number from (1).

• 4. Factor and simplify.
• 5. To graph from vertex form, follow what we learned last lesson about step

pattern OR use the y­intercept to graph.

MPM2D1 ­ U3L2 ­ Graphing Quadratic Functions 6

a) y = x2 + 12x ­ 7

• Ex. 5 Complete the Square for the following:

b) y = ­3x2 + 4x

c) y = ­1x2 + 2x + 4 3

d) y = 0.2x2 + 1.6x + 3.1

MPM2D1 ­ U3L2 ­ Graphing Quadratic Functions 7

Homework Quadratic Functions Booklet p.224 #13 p.234­238 #2p2, 3, (4 ­ 9)p2, 24, 25