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### Chapter 10 Sec 1

Graphing Quadratic Functions

The seven steps to graphing.f(x) = ax2 +bx + c

- Find a = , b = , c = .
- Find y intercept = (0, c).
- Find Axis of Symmetry
- Find Vertex ( AOS , __ )
- Plug AOS in function to find y.
- Look at ais it (+) min or (-) max
- Find Value Max/Min (y of vertex).
- Make Table of Values and Plot put vertex in the center of the table and graph.

Quadratic Function

A quadratic function is described by an equation of the following form.

Linear term

Constant term

Quadratic term

The graph of any quadratic function is called a parabola..

Graph of Parabola

Similar to Pg 526

Axis of Symmetry and y - intercept

Find the y-intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then graph. f(x) = x2 + 9 + 8x

Step 1: Arrange terms. Then identify a, b, and c

f(x) = x2 + 9 + 8x

f(x) = x2 + 8x + 9

So a = 1, b = 8, and c = 9

Step 2: Find the y-intercept, (0, c)

The y-intercept is (0, 9).

Step 3: Find the Axis of Symmetry (AOS)

AOS = -4

Vertex and Graph

Find the y-intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then graph. f(x) = x2 + 8x + 9

Step 4: Find the coordinates of the vertex. (AOS, ___).

Plug AOS in original function to find y - coordinate

f(-4) = x2 + 8x + 9

= (-4)2 + 8(-4) + 9 = 16 - 32 + 9 = -7

Step 5: Max or Min a = 1, positive so Minimum

Step 6: Value of Max/Min:

(-4, -7)

vertex

–7

Min: –7

Vertex and Graph

Find the y-intercept, the equation of the axis of symmetry, the vertex , Max or min and Value, then graph. f(x) = x2 + 8x + 9

(-4, -7)

vertex

vertex

Find Max or Min

To find Max/Min without graphing do Steps 1 – 6.

Step 1. a = 1, b = – 4, and c = 9

Step 2. y–intercept (0, 9)

Step 3.

Step 4. Find Vertex (2, __)

f(2) = (2)2 - 4(2) + 9 = 4 - 8 + 9 = 5

Step 5. Max/Min? a = 1. a is positive minimum value.

Step 6. Value of Max/Min. The Vertex is (2, 5) So the

Min value is 5.

Consider the function f(x) = x2 - 4x + 9

5

The seven steps to graphing.f(x) = ax2 +bx + c

- Find a = , b = , c = .
- Find y intercept = (0, c).
- Find Axis of Symmetry
- Find Vertex ( AOS , __ )
- Plug AOS in function to find y.
- Look at a is it (+)min or (-)max
- Find Value Max/Min (y of vertex).
- Make Table of Values and Plot put vertex in the center of the table and graph.

Daily Assignment

- Chapter 10 Section 1
- Study Guide (SG)
- Pg 131 - 132 All

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