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Find the coordinates of the minimum point of the curve y=x^2+6x+5.

To answer this question is equivalent to minimising y=(x+3)^2-4. We have that all square numbers are greater than or equal to 0 so to minimise this equation, we require that (x+3)^2=0. This is satisfied only...
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Answered by Jonny I. Maths tutor
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Factorise x^2+6x+5=0 by completing the square.

When completing the square, we first divide the whole equation by the x^2 component. In this case, the x^2 component is 1 so nothing changes. We now apply the method to convert to square form: we reduce the ...
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Answered by Jonny I. Maths tutor
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Find the coordinates where the curve y=x^2+6x+5 crosses the x-axis.

When any curve crosses the x-axis, the y-coordinate is 0 at that point. Hence, our answers will have y=0. So we want to solve x^2+6x+5=0. From before, we have that x^2+6x+5=0 can be rewritten as (x+5)(x+1)=0...
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Answered by Jonny I. Maths tutor
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Factorise fully x^2+6x+5=0

To start, notice that we have x^2 in our equation. This means that our answer is of the form (x )(x ). We now look for integers that give 5 when multiplied together. The only way we can do this is with the n...
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Answered by Jonny I. Maths tutor
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Simplify the following expression to a fraction in its simplest form: [(4x^2 + 6x)/(2x^2 - x -6)] - [(12)/(x^2 - x - 2)]

2(x+3)/(x+1)
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Answered by Dylan H. Maths tutor
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