📊 Part 1: Identifying Quadratic Equations

1. Circle the equations that are quadratic equations:

x² - 4x - 21 = 0

3x + 7 = 0

2x² + 5x - 3 = 0

x³ - 2x + 1 = 0

2. For the quadratic equation x² - 6x + 8 = 0, identify the values:

a = ______ b = ______ c = ______

3. Rewrite these equations in standard form (ax² + bx + c = 0):

a) x² = 4x + 21 Answer: _________________________

b) 3x² - 7 = 2x Answer: _________________________

🔢 Part 2: Solving by Factoring

4. Solve x² - 4x - 21 = 0 by factoring. Show all working:

5. Factor and solve these quadratic equations:

a) x² + 7x + 12 = 0

b) x² - 9x + 20 = 0

c) x² - 25 = 0

6. Explain the zero product property in your own words:

📐 Part 3: The Quadratic Formula

7. Write out the quadratic formula:

x = _________________________________

8. Use the quadratic formula to solve 2x² + 3x - 2 = 0. Show all steps:

9. For each equation, calculate the discriminant (b² - 4ac) and predict the number of solutions:

a) x² - 6x + 9 = 0

Discriminant = ______ Number of solutions: ______

b) x² + 2x + 5 = 0

Discriminant = ______ Number of solutions: ______

c) x² - 3x - 4 = 0

Discriminant = ______ Number of solutions: ______

📈 Part 4: Connecting Algebra and Graphs

10. Match each quadratic equation with the correct description of its graph:

1. x² - 4x + 4 = 0

2. x² - 5x + 6 = 0

3. x² + x + 1 = 0

A. Parabola crosses x-axis twice

B. Parabola touches x-axis once

C. Parabola doesn't touch x-axis

11. The solutions to a quadratic equation are x = 2 and x = -3. What do these values represent on the graph of the parabola?

The y-intercepts

The x-intercepts

The vertex coordinates

The maximum points

12. Sketch a rough graph of y = x² - 4x - 21 and mark the x-intercepts:

🎯 Part 5: Choosing the Best Method

13. For each equation, tick which method would be most efficient to solve it:

a) x² - 16 = 0

Factoring

Quadratic Formula

Square Root Method

b) 3x² + 2x - 7 = 0

Factoring

Quadratic Formula

Square Root Method

c) x² - 8x + 15 = 0

Factoring

Quadratic Formula

Square Root Method

14. Challenge Problem: A ball is thrown upward from a height of 2 metres. Its height h (in metres) after t seconds is given by h = -5t² + 20t + 2. When does the ball hit the ground? (Hint: When does h = 0?)

🔍 Part 6: Reflection

15. Which method for solving quadratic equations do you find easier and why?

16. Explain how the discriminant helps you understand what the graph of a quadratic function will look like:

Solving Quadratic Equations

Solving Quadratic Equations

📊 Part 1: Identifying Quadratic Equations

🔢 Part 2: Solving by Factoring

📐 Part 3: The Quadratic Formula

📈 Part 4: Connecting Algebra and Graphs

🎯 Part 5: Choosing the Best Method

🔍 Part 6: Reflection

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