Question

Igcse math(quadratic functions)

curve: y = x^2+2x
line: y = 4 - 2x
a, Determine if the line intersects the curve, is a tangent to the curve or does not meet the curve.
b, Give the coordinates of any points where the line and curve touch or intersect.

Answer 1

Below in bold.

Explanation:

a) Solve the system of equations:

y = x^2 + 2x

y = 4 - 2x so,

x^2 + 2x = 4 - 2x (as they are both equal to y)

x^2 + 4x - 4 = 0

x = [-4 +/- sqrt((-4)^2 - 4*1*-4)] / 2

= -2 +/- sqrt32 / 2

= 0.828, -4.828

The line intersects the curve at 2 points.

b. Substitute x = 0.828 and -4.8128 into y = 4 - 2x will give the y coordinates of the 2 points.

These points are (0.828, 2.343) and (-4.828, 13.657).