The trajectory of a subterranean mining probe is modeled by the function y=p(x)y = p(x)y=p(x), where xxx represents horizontal distance and yyy represents vertical position relative to a baseline. The probe's path forms a V-shape, descending to its lowest point at the vertex (7,−5)(7, -5)(7,−5) and intersecting the vertical axis at the point (0,2)(0, 2)(0,2).
Identify which one of the four equations listed below is the correct equation of the probe's trajectory.
□y=∣x−7∣+5\square \quad y = |x - 7| + 5□y=∣x−7∣+5
□y=∣x+7∣−5\square \quad y = |x + 7| - 5□y=∣x+7∣−5
□y=∣x−7∣−5\square \quad y = |x - 7| - 5□y=∣x−7∣−5
□y=∣x+7∣+5\square \quad y = |x + 7| + 5□y=∣x+7∣+5
471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.