A model for the elevation EEE (in decameters) of a section of a mountain range relative to a baseline is given by a polynomial function E=h(d)E = h(d)E=h(d), where ddd is the horizontal distance (in km) from a lookout point.
A sketch of the curve y=h(d)y = h(d)y=h(d) shows that it passes through the point (0,10)(0, 10)(0,10) on the yyy-axis and touches the xxx-axis at a minimum turning point (4,0)(4, 0)(4,0). There is a maximum turning point at (−4,16)(-4, 16)(−4,16). The function behaves like a positive cubic, falling as d→−∞d \rightarrow -\inftyd→−∞ and rising as d→∞d \rightarrow \inftyd→∞.
On separate diagrams, sketch the curve with the following equations:
y=2h(d−4)y = 2h(d - 4)y=2h(d−4)
y=h(2d)−10y = h(2d) - 10y=h(2d)−10
On each sketch, show clearly the coordinates of:
566 exam-style questions on OCR A Level Maths 1.2 Algebra and Functions, covering 1.2.1 Indices, 1.2.2 Surds, 1.2.3 Simultaneous equations, 1.2.4 Quadratic functions, 1.2.5 Completing the square, 1.2.6 Solving quadratic equations, 1.2.7 Inequalities, 1.2.8 Expressing solutions of inequalities, 1.2.9 Representing inequalities graphically, 1.2.10 Manipulating polynomials, 1.2.11 Simplifying rational expressions, 1.2.12 The modulus function (A-level only), 1.2.13 Graphs of functions, 1.2.14 Sketching curves from equations, 1.2.15 Sketching reciprocal curves, 1.2.16 Interpreting solutions graphically, 1.2.17 Intersection points of graphs, 1.2.18 Proportional relationships, 1.2.19 Graph of the modulus of a linear function (A-level only), 1.2.20 Solving modulus equations graphically (A-level only), 1.2.21 Definition of a function (A-level only), 1.2.22 Inverse and composite functions (A-level only), 1.2.23 Simple graph transformations, 1.2.24 Combinations of graph transformations (A-level only), 1.2.25 Partial fractions (A-level only), and 1.2.26 Models in context. Each one has a worked solution and a mark scheme showing where the marks go.