Find the values of x where the curve y = 8 -4x-2x^2 crosses the x-axis.
A curve crosses the x-axis when y=0, if we put that into the equation above we get the quadratic equation 0=8-4x-2x2. The solutions to this equation are the values of x where y=0, which is the same as saying the values of x where the curve crosses the y axis, so the solutions to this equation are our answers. We can solve the equation using the quadratic formula, x=(-b+√(b2-4ac))/2a or x=(-b-√(b2-4ac))/2a. In this equation a=-2, b=-4, c=8, which gives x=(-(-4)+√((-4)2-4*(-2)8))/2(-2) or (-(-4)+√((-4)2-4*(-2)8))/2(-2). Simplified this is x=(4+√80)/-2 or x=(4-√80)/-4, which again simplifies to x=-1+√5 or x=-1-√5. So these are values of x where the curve y=8-4x-2x^2 crosses the x-axis.
HW
Related Maths A Level answers
All answers ▸Find the x and y coordinates of the turning points of the curve 'y = x^3 - 3x^2 +4'. Identify each turning point as either a maximum or a minimum.
A curve C has equation y = x^2 − 2x − 24 x^(1/2), x > 0 (a) Find (i) dy/d x (ii) d^2y/dx^2 (b) Verify that C has a stationary point when x = 4 (c) Determine the nature of this stationary point, giving a reason for your answer.
Express the equation cosecθ(3 cos 2θ+7)+11=0 in the form asin^2(θ) + bsin(θ) + c = 0, where a, b and c are constants.
Given y = x^3 + 4x + 1, find the value of dy/dx when x=3