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2.1 – Quadratic Functions

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**In this section, you will learn to**

analyze graphs of quadratic functions write quadratic functions in standard form and sketch its graphs solve real-life problems

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**Definition of a Polynomial Function:**

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**Definition of a Quadratic Function:**

a) Axis of symmetry: the line where the parabola is symmetric b) Vertex: The point where the axis of symmetry intersects the parabola

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**Definition of a Quadratic Function:**

c) Upward or Downward: If the leading coefficient is positive (a>0) , the parabola opens upward.

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**Definition of a Quadratic Function:**

c) Upward or Downward: If the leading coefficient is negative (a<0) , the parabola opens downward.

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**Definition of a Quadratic Function:**

d) Minimum or Maximum: If the parabola opens upward, the vertex has a minimum value. If the parabola opens downward, the vertex has a maximum value.

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**Standard Form of a Quadratic Function:**

a) Vertex: b) Axis of Symmetry: c) Vertex: Therefore, * To write an equation in standard form, you need to complete the square.

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**Identify the vertex and axis of symmetry for**

There are two methods to identify the vertex and the axis of symmetry. Method 1:

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**Method 2: Complete the Square**

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Complete the Square:

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**Method 2: Complete the Square**

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**Identify the vertex and zeros to graph:**

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**Identify the vertex and zeros to graph:**

Vertex: Zeros:

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**Find the quadratic equation in standard form:**

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**Find the quadratic equation in standard form:**

Vertex: Point:

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Real-Life Example:

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Real-Life Example: Since this parabolic path is opening downward, the maximum height is reached at the vertex point. You can use the formulas for h and k to find the vertex point. Then, the maximum height is represented by the k value.

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Real-Life Example: The maximum height reached by this ball is 130 ft.

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Graph: The maximum height reached by this ball is 130 ft.

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Real-Life Example:

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Real-Life Example: Since this parabolic path is opening upward, the minimum height is reached at the vertex point. You can use the formulas for h and k to find the vertex point. Then, the minimum height is represented by the k value.

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Real-Life Example: The minimum height reached by the yo-yo is 16 feet.

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Real-Life Example: The minimum height reached by the yo-yo is 16 feet.

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