Mathematics

Curved Graphs Quiz: Marking Scheme This is the marking scheme for quiz: M18 - Curved Graphs Quiz Topic Guide: M18 - Curved Graphs Total: 40 marks Accept equivalent notation and correct methods that produce a correct result. A — $y=(x-2)^2-3$ B — reciprocal graph with two branches B — $x=3$ C — tangent has the same gradient as the curve at the point of contact For $y=x^2-6x+5$: 1 mark: Finds the axis of symmetry as $x=3$, using $x=-b/(2a)$ or an equivalent method. 2 marks: Finds the turning point as $(3,-4)$. 1 mark for substituting $x=3$ correctly. 1 mark for obtaining $y=-4$ and stating the coordinates. 1 mark: Identifies the turning point as a minimum because the coefficient of $x^2$ is positive. For $y=-3/x$: ...

Curved Graphs Quiz Total: 40 marks Answer all questions. Show working for Questions 5–8. Give exact answers where appropriate. 1. [1 mark] A quadratic function has its vertex at $(2,-3)$ and passes through $(4,1)$. Which equation represents the function? A. $y=(x-2)^2-3$ B. $y=(x-2)^2+3$ C. $y=2(x-2)^2-3$ D. $y=(x+2)^2-3$ 2. [1 mark] What type of graph is represented by $y=\frac{1}{x}$? A. A straight line B. A reciprocal graph with two branches ...