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Linear Quadratic Graphs Features

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Linear Quadratic Graphs Features worksheet preview

Linear Quadratic Graphs Features

Linear and quadratic graphs illustration

📊 Part 1: Identifying Graph Features

1. Which equation represents a quadratic function?

y = 3x + 5

y = x² - 4

y = 2x - 1

y = -x + 7

2. For the equation y = -2x² + 8, the parabola opens:

Upwards (because a is positive)

Downwards (because a is negative)

Sideways

Cannot be determined

3. What is the y-intercept of the equation y = x² - 3x + 2?

(0, 3)

(0, 2)

(0, -3)

(2, 0)

4. A quadratic graph can have:

Zero x-intercepts

One x-intercept

Two x-intercepts

Three x-intercepts

🔢 Part 2: Calculating Key Features

5. For the quadratic equation y = x² - 6x + 5, find the vertex.

Step 1: Find x-coordinate using x = -b/(2a)

a = _____, b = _____, c = _____

x = -(_____) ÷ (2 × _____) = _____

Step 2: Find y-coordinate by substituting x back into the equation:

Vertex coordinates: ( _____, _____ )

6. Find where the graphs y = x + 1 and y = x² - 3 intersect.

Set equations equal: x + 1 = x² - 3

Rearrange: x² - x - 4 = 0

Intersection points: ( _____, _____ ) and ( _____, _____ )

📈 Part 3: Graph Analysis

7. Sketch the graph of y = -x² + 4 and label the key features.

Mark and label:

• Vertex: ( _____, _____ )

• Y-intercept: ( _____, _____ )

• X-intercepts: ( _____, _____ ) and ( _____, _____ )

• Direction of opening: _____________

8. Explain why a quadratic graph can have two x-intercepts but a linear graph can only have one.
9. A projectile is launched and follows the path y = -5x² + 20x + 3, where x is time in seconds and y is height in metres.

a) What is the initial height of the projectile? _____ metres

b) At what time does the projectile reach its maximum height? _____ seconds

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