Quadratic Equations Worksheet

Name:

Date:

🎯 WALT: Form and solve quadratic equations

Success Criteria: I can write quadratic equations, solve them by factorisation, and explain the zero product property.

1. Which of these is a quadratic equation in standard form?

y = 2x + 5

x² - 3x + 2 = 0

y = x³ + 1

2x + y = 10

2. Solve by factorisation: x² - 5x + 6 = 0

Solutions: x = _______ and x = _______

3. Rearrange to standard form, then solve: x² = 4x - 3

Solutions: x = _______ and x = _______

4. A rectangular garden has length (x + 4) metres and width (x - 2) metres. If the area is 15 square metres, form a quadratic equation to find x.

Equation: ___________________________ = 0

Value of x: _______

📊 Part 2: Graphs and Solutions

5. How many solutions does each quadratic equation have based on its graph?

a) A parabola that crosses the x-axis twice: _______ solutions

b) A parabola that touches the x-axis once: _______ solution(s)

c) A parabola that doesn't touch the x-axis: _______ solutions

6. The quadratic equation x² - 6x + 9 = 0 has solutions where the parabola crosses the x-axis. Solve this equation and describe what this means for the graph.

Number of solutions: _______

This means the parabola _________________________________ the x-axis.

7. Explain the zero product property in your own words. Why do we set quadratic equations equal to zero when solving?

🌍 Part 3: Real-Life Applications

8. A rugby ball is kicked upward. Its height h (in metres) after t seconds is given by h = -5t² + 20t + 1. When does the ball hit the ground?

Hint: The ball hits the ground when h = 0

The ball hits the ground after _______ seconds.

9. Extension: A company's profit P (in hundreds of dollars) is modelled by P = -2x² + 12x - 10, where x is the number of products sold (in thousands). Find the number of products that must be sold to break even (profit = 0).

Break-even points: _______ thousand and _______ thousand products

10. Create your own real-life problem that could be solved using a quadratic equation. Write the problem and show how to set up the equation.