Quadratic and non-linear simultaneous equationsIB MYP Maths Extended: Mind map

Exam questions on Quadratic and non-linear simultaneous equations

1. Consider the line $y=x+2$ and the curve $y=x^2$.
   The line is replaced by $y=2x-1$. Show that this new line meets the curve $y=x^2$ at exactly one point, and state the coordinates of that point.2 marks
2. Consider the line $y=3x-4$ and the curve $y=x^2-4x+8$.
   The line is changed to $y=2x-2$. Show that it does not meet the curve $y=x^2-4x+8$.2 marks
3. A rectangular patio has length $x$ m and width $y$ m. Its perimeter is $20$ m and its area is $21$ m$^2$.
   Show that $x^2-10x+21=0$.3 marks