2.5

Quadratics

9 flashcards to master Quadratics

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Definition Flip

Answer Flip

Key Concept Flip

Explain how to solve a quadratic equation by factorisation. Give an example.

Answer Flip

Factorisation involves expressing the quadratic as a product of two linear factors.

Example: x² + 5x + 6 = (x+2)(x+3) = 0. Solutions are x = -2 and x = -3 (set each factor to zero).
Key Concept Flip

State the quadratic formula and explain when it is most useful.

Answer Flip

The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a. It's most useful when the quadratic equation is difficult or impossible to factorise easily, or to verify factorisation.

Key Concept Flip

Answer Flip

Definition Flip

Answer Flip

Definition Flip

What is the turning point (vertex) of a parabola, and how does it relate to the minimum or maximum value?

Answer Flip

The turning point, or vertex, is the point where the parabola changes direction. It represents the minimum y-value if the coefficient of x² is positive (opens upwards), and the maximum y-value if it's negative (opens downwards).

Example: the parabola y = x² - 4x + 3 has a turning point at (2, -1), which is the minimum y-value.
Key Concept Flip

Topic: Quadratics. Question: How do you find the axis of symmetry of a parabola given its equation?

Answer Flip

The axis of symmetry is a vertical line passing through the vertex. Its equation is x = -b / 2a, where 'a' and 'b' are coefficients from the quadratic equation in the form ax² + bx + c = 0.

Example: For y = x² + 4x + 3, the axis of symmetry is x = -4 / (2*1) = -2.
Key Concept Flip

Explain the process of completing the square for the quadratic expression x² + 6x + 5. Express in form (x + p)² + q.

Answer Flip

To complete the square: (x + 3)² - 9 + 5 = (x + 3)² - 4. The expression is now in the form (x+p)² + q, where p = 3 and q = -4. This form readily reveals the vertex coordinates.

Key Concept Flip

A quadratic equation has roots at x = 2 and x = -3. Determine the equation in the form ax² + bx + c = 0.

Answer Flip

If roots are 2 and -3, the factors are (x-2) and (x+3). Expanding (x-2)(x+3) gives x² + x - 6 = 0. So, a=1, b=1, and c=-6.

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2.4 Sequences 2.6 Graphs of functions

Key Questions: Quadratics

What is the turning point (vertex) of a parabola, and how does it relate to the minimum or maximum value?

The turning point, or vertex, is the point where the parabola changes direction. It represents the minimum y-value if the coefficient of x² is positive (opens upwards), and the maximum y-value if it's negative (opens downwards).

Example: the parabola y = x² - 4x + 3 has a turning point at (2, -1), which is the minimum y-value.

About Quadratics (2.5)

These 9 flashcards cover everything you need to know about Quadratics for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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