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Give an example of a real-world system that would be described by a quadratic equation. Explain the significance of the two real roots, a repeated root, and undefined roots. Is there any significance to a positive or a negative answer in your example?

For a ball that has been thrown, it's height above the ground can be described by a quadratic equation of the time since it was thrown and gives a parabola.

The two real roots of the equation are t...

Answered by James B. • Maths tutor

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How can i use completing the square to factorise and solve equations

This method will only work if your x term is divisible by 2. For example x² + 6x + 12.

You then use the halved x term (e.g. 3x) to complete the square. The beginning of your factorisat...

Answered by Natalie S. • Maths tutor

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Simplify (x + 3)(2x + 5) - (x - 1)

Start by expanding the brackets: 2x^2 + 5x + 6x + 15 = 2x^2 +11x + 15 Combine the two parts of the equation: 2x^2 + 11x + 15 - x + 2 = 2x^2 + 10x + 17

Answered by Hannah M. • Maths tutor

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Fully simplify: (y^2 x y^5) / y^3

(y²x y⁵) / y³ When multiplying, the indices must be added together, therefore y² x y⁵ = y²⁺⁵ = y⁷ (y²x y⁵

Answered by Jemima P. • Maths tutor

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Increase £160 by 45%.

If £160 = 100%, the number we are trying to find (let's call this X) equals 145%. (Place numbers in 2x2 grid) 100% £160 145% X Multiply the two diagonal numbers together, then divide by the number ...

Answered by Jemima P. • Maths tutor

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