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Given the curve y=x^2 -6x +8, find the turning point.

For a turning point, the differential of the curve is equal to 0. Therefore dy/dx = (12)x^(2-1) - (61)x^(1-1) + 0 = 0. This gives x = 3. Substitute this back into the original equation to get y=-...

Answered by Ellis B. • Maths tutor

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Expand and simplify fully (x+3)(x-1)

When expanding brackets one should follow the FOIL order, multiplying out in this order:First- The first term in each bracket Outside- The outside terms of the brackets

Answered by Callum L. • Maths tutor

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Factorise x^2+3x+4 without the use of quadratic formula

We use the form ax^2+bx+cTo factorise we need to put the equation into 2 bracketsThese 2 brackets will be in the form (x+k)(x+j) where k and j are to be foundWe need to find a combination of k and j for w...

Answered by William C. • Maths tutor

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f(x)=12x^2e^2x - 14, find the x-coordinates of the turning points.

f(x)=(12x^2)(e^2x) - 14, so using the chain rule f'(x)=(24x)(e^2x) + (12x^2)(2e^2x).To find the turning points set f'(x)=0, so (24x)(e^2x) + (24x^2)(e^2x) = 0. Thus (24xe^2x)(1+x)=0. Thus x=0 or x=-1.

Answered by Charlotte H. • Maths tutor

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Solve algebraically the simultaneous equations x^2 + y^2 = 25 and y - x = 1

Let's label the equations x² + y² = 25 (1) y - x = 1 (2). We can use substitution to solve this simultaneous equation. Let's make y the subject of the equation (2) and we get y = x...

Answered by Vithya N. • Maths tutor

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