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Find the vertex coordinates of parabola y = 2x^2 - 4x + 1

In this exercise I have to find the coordinates of the vertex of the parabola. Given the general equation y= ax^2 + bx + c , the value of a is 2, the value of b is -4 and the value of c is 1. In order to com...
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Answered by Martina B. • Maths tutor
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How do you complete the square to answer quadratic equations?

x 2 +6x-2 = 0 We use completing the square when the equation cannot be factorised. Begin by placing x 2 in the brackets and halving the number in front of the x (also known as the coefficient of x) to form (...
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Answered by Mikhailia M. • Maths tutor
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y is inversely proportion to the square of x. y=10 when x=5. Express y in terms of x.

y is proportion to 1/x 2 . This can be written as y=k/x 2 where k is a constant of proportionality. Given that y=10 when x=5 , k can be found as yx 2 which is equal to 25. Therefore; y=25/x 2 .
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Answered by Evan H. • Maths tutor
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The curve y = 2x^3 - ax^2 + 8x + 2 passes through the point B where x=4. Given that B is a stationary point of the curve, find the value of the constant a.

As B is a stationary point, the value of dy/dx at this point must be equal to 0. Differentiating y gives this to be dy/dx = 6x 2 -2ax+8. At point B , x=4 . This gives the relation 104=8a and thus gives a=13.
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Answered by Evan H. • Maths tutor
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How would one multiply out brackets?

If asked to multiply out a set of brackets, one must remember to multiply each term in a set of brackets by every term in the other set of brackets. For example, (x+2)(x-4) = x 2 +2x-4x-8 = x 2 -2x+8. An inc...
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Answered by Alden R. • Maths tutor
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