📊 Part 1: Quadratic Forms Recognition

1. Identify which form each quadratic function is written in:

a) f(x) = 2(x - 3)² + 5

Standard form

Vertex form

Factored form

b) g(x) = x² - 6x + 8

Standard form

Vertex form

Factored form

c) h(x) = 3(x + 2)(x - 4)

Standard form

Vertex form

Factored form

2. For the quadratic f(x) = -2x² + 8x - 6, what can you determine directly from this form?

The y-intercept is -6

The parabola opens downward

The vertex is at (2, 2)

The zeros are x = 1 and x = 3

3. Which coefficient in the standard form ax² + bx + c determines whether the parabola opens upward or downward?

a

b

c

🔄 Part 2: Converting Between Forms

4. Convert f(x) = x² - 4x + 3 to vertex form by completing the square.

5. Convert f(x) = x² - 4x + 3 to factored form.

6. From your work above, identify the following key features:

Vertex: ( _____ , _____ )

Zeros/x-intercepts: x = _____ and x = _____

y-intercept: _____

Axis of symmetry: x = _____

🌟 Part 3: Real-World Applications

7. A baseball is hit and follows the path h(t) = -16t² + 64t + 4, where h is the height in feet and t is time in seconds.

a) What is the initial height of the baseball? _____ feet

b) At what time does the baseball reach its maximum height?

c) What is the maximum height reached?

8. Explain in your own words why vertex form a(x - h)² + k is useful for identifying the vertex of a parabola.

9. How does changing the value of 'a' in a quadratic function affect the shape of the parabola? Give at least two specific effects.

Quadratic Functions Exploration

Quadratic Functions Exploration

📊 Part 1: Quadratic Forms Recognition

🔄 Part 2: Converting Between Forms

🌟 Part 3: Real-World Applications

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