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Chapter 10 Sec 1. Graphing Quadratic Functions. The seven steps to graphing. f ( x ) = ax 2 + 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

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Chapter 10 Sec 1

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Chapter 10 sec 1

Chapter 10 Sec 1

Graphing Quadratic Functions


The seven steps to graphing f x ax 2 bx c

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

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

Graph of Parabola

Similar to Pg 526


Max and min values

Max and Min Values


Axis of symmetry and y intercept

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

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 graph1

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


Graph f x x 2 8x 9

Graph f(x) = x2 + 8x + 9

y-intercept

(0, 9)

x = -4

AOS

x = -4


Find max or min

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 ax 2 bx c1

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

Daily Assignment

  • Chapter 10 Section 1

    • Study Guide (SG)

      • Pg 131 - 132 All


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