A curve is given by the equation y=x^3-11x^2+28x; find the coordinates of the points where the curve touches the x-axis.

Since the equation has a cubic term, we can expect the curve to have certain properties: it should have three points where the graph touches the x-axis, two turning points, of which one should be a minimum and one should be a maximumTo start we will find the point where the curve touches the x-axis and to do that we have to simplify the equation of the curve by factorising it, since every term has an x value, we can factorise the whole equation by x, giving us x(x^2-11x+28). Now we have a quadratic equation which we can factorise by sight or by using the quadratic equation, to give us y=(x)(x-4)(x-7), this tells us that when the curve touches the x-axis (when y=0) x = 0, 4, 7, therefore the coordinates are (0,0), (4,0) and (7,0)

Answered by Lui H. Maths tutor

2557 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

The perimeter of an isosceles triangle is 16cm. The length of the base of the triangle is x+4 and that of the other two sides is x+3. Find the area of the triangle


Draw y=x^2+5


given that f(x) = x^4 + 2x, find f'(x)


In a village the number of houses and the number of flats are in the ratio 7 : 4 the number of flats and the number of bungalows are in the ratio 8 : 5 There are 50 bungalows in the village. How many houses are there in the village?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo
Cookie Preferences