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Maths
GCSE

Factorise 2e – 4f + ex -2fx

2(e-2f) + x(e-2f) = (2+x)(e-2f)

Answered by Katrina T. Maths tutor
4263 Views

Sketch the curve y=4-(x+3)^2, showing the points where the curve crosses the x-axis and any minimum or maximum points.

This equation rearranges to give -y=(x+3)^2-4, which is very similar to our curve y=(x+3)^2-4 from before. In fact, replacing y with -y in an equation is equivalent to reflecting the curve through the x-a...

Answered by Jonny I. Maths tutor
3279 Views

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 o...

Answered by Jonny I. Maths tutor
11019 Views

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 t...

Answered by Jonny I. Maths tutor
8326 Views

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...

Answered by Jonny I. Maths tutor
3944 Views

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