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Completing the Square

A curve has an equation y = 2x 2 – 5x + 12 a. Write y = 2x 2 – 5x + 12 in the form a(x + m) 2 + n b. Find the coordinates of the minimum point of the graph. c. Does the graph of y = 2x 2 – 5x + 12 , cross th...
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Answered by Andre d. • Maths tutor
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Solve the simultaneous equations. 5x + y = 21 and x-3y = 9

Label the equations, [a] 5x + y =21 and [b] x-3y =9. [b]: x - 3y = 9, [c]: x = 3y + 9. Substitute [c] into [a] 5(3y + 9) + y = 21 , 16y + 45 = 21 16y = -24 , y = - 3/2. Substitute y = -3/2 into [b]: x + 9/2 ...
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Answered by Solomon K. • Maths tutor
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The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.

The first step should be to rearrange the equation of the perpendicular line to PQ, in order to find the gradient, which works out to -3/2x. This can be done using the equation y=mx+c, where m is the gradien...
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Answered by M D. • Maths tutor
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What is cuberoot(64x1000)?

This is a question from a non calculator GCSE paper only answered correctly by roughly half the students. The question is regarding the topic of surds and is quite a basic question testing your knowledge on ...
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Answered by Avik J. • Maths tutor
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Factorise the expression x^2+5x-24.

Using the general form of a quadratic equation ax 2 +bx+c, we known that ax 2 +bx+c=(x+d)(x+e).The constant term, c, must be equal to the product of our two constants in the factorisation, therefore c=d x e....
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Answered by Louis C. • Maths tutor
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