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Polynomials and Quadratics

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Polynomials and Quadratics

Quadratic parabola graph

📚 Part 1: Understanding Polynomials

1. Which of the following are quadratic polynomials?

3x + 5

x² + 4x - 7

2x³ + x² + 1

-x² + 9

2. What is the degree of the polynomial 5x³ - 2x² + 7x - 1?

1

2

3

4

3. Classify each polynomial by the number of terms:

a) 3x² _________________ (monomial/binomial/trinomial)

b) x² + 5x - 2 _________________ (monomial/binomial/trinomial)

c) 4x - 7 _________________ (monomial/binomial/trinomial)

✏️ Part 2: Expanding and Factorising

4. Expand the following expressions:

a) (x + 3)(x + 2) = _________________

b) (x - 4)(x + 1) = _________________

c) (x + 5)(x - 5) = _________________

5. Factorise these quadratic expressions:

a) x² + 8x + 15 = _________________

b) x² - 25 = _________________

c) x² + 6x + 9 = _________________

6. Show your working to factorise x² + 9x + 20:

🎯 Part 3: Solving and Graphing

7. Solve these quadratic equations by factorising:

a) x² + 7x + 12 = 0

x = _____ or x = _____


b) x² - 16 = 0

x = _____ or x = _____

8. For the quadratic y = (x - 2)(x + 4):

a) The x-intercepts (roots) are: x = _____ and x = _____

b) The axis of symmetry is the line: x = _____

c) Does the parabola open upward or downward? _____________

9. Sketch the graph of y = (x - 1)(x - 3) below. Mark the x-intercepts, axis of symmetry, and vertex.
10. Explain in your own words: How are the roots of a quadratic equation related to the x-intercepts of its graph?

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