📊 Part 1: Understanding Quadratic Expressions

1. Circle the expressions that are quadratic:

y = 3x + 5

y = x² + 2x - 1

y = 2x² - 4

y = 5x - 3

2. For the quadratic expression y = 2x² + 3x - 5, identify the coefficients:

a = _______ (coefficient of x²)

b = _______ (coefficient of x)

c = _______ (constant term)

3. Match each quadratic expression with its correct description:

1. y = x²

2. y = -x² + 4

3. y = 2x² + x - 3

A. Opens downward with vertex at (0,4)

B. Simple parabola through origin

C. Has all three terms: ax², bx, and c

📈 Part 2: Creating Tables of Values

4. Complete the table of values for y = x² - 4:

Fill in the missing y-values:

When x = -2: y = (-2)² - 4 = _____ - 4 = _____

When x = -1: y = (-1)² - 4 = _____ - 4 = _____

When x = 0: y = (0)² - 4 = _____ - 4 = _____

When x = 1: y = (1)² - 4 = _____ - 4 = _____

When x = 2: y = (2)² - 4 = _____ - 4 = _____

5. Using your table from question 4, what are the roots (x-intercepts) of y = x² - 4?

🎨 Part 3: Sketching Quadratic Graphs

6. Using the values from question 4, sketch the graph of y = x² - 4 on the grid below:

7. Describe the shape of your graph:

Straight line

U-shaped curve (parabola)

Circle

Zigzag pattern

8. Check all the properties that apply to quadratic graphs:

They are always U-shaped or upside-down U-shaped

They are straight lines

They have a highest or lowest point called the vertex

They are symmetrical

They can cross the x-axis at most twice

🌍 Part 4: Real-World Applications

9. A ball is thrown upward and its height h (in metres) after t seconds is given by h = -5t² + 20t + 2. Complete the following:

When t = 0 seconds: h = -5(0)² + 20(0) + 2 = _____ metres

When t = 1 second: h = -5(1)² + 20(1) + 2 = _____ metres

When t = 2 seconds: h = -5(2)² + 20(2) + 2 = _____ metres

10. Circle the real-world situations that could be modelled by quadratic equations:

The path of a football when kicked

The speed of a car travelling at constant velocity

The area of a square garden with side length x

The trajectory of a rocket

11. Explain in your own words what makes a quadratic equation different from a linear equation:

🔍 Part 5: Key Vocabulary

12. Fill in the blanks using the words from the box:

Word Bank: parabola, vertex, roots, coefficient, quadratic

A _____________ equation contains a term with x². The graph of a quadratic equation is called a _____________. The highest or lowest point on this graph is called the _____________. The points where the graph crosses the x-axis are called the _____________. In the expression 3x² + 2x - 1, the number 3 is the _____________ of x².

13. Draw and label a simple parabola showing the vertex and roots: