f(x)=3x2+18x+31x∈Rf(x) = 3x^2 + 18x + 31 \quad x \in \mathbb{R}f(x)=3x2+18x+31x∈R
Write f(x)f(x)f(x) in the form a(x+b)2+ca(x + b)^2 + ca(x+b)2+c, where aaa, b b\,b and c c\,c are integers to be found.
Sketch the curve with equation y=f(x)y = f(x)y=f(x) showing any points of intersection with the coordinate axes and the coordinates of any turning point.
Describe fully the transformation that maps the curve with equation y=f(x)y = f(x)y=f(x) onto the curve with equation y=g(x)y = g(x)y=g(x) where
g(x)=3(x−2)2+18x−5x∈R g(x) = 3(x - 2)^2 + 18x - 5 \quad x \in \mathbb{R} g(x)=3(x−2)2+18x−5x∈RFind the range of the function
h(x)=203x2+18x+31x∈R h(x) = \frac{20}{3x^2 + 18x + 31} \quad x \in \mathbb{R} h(x)=3x2+18x+3120x∈R471 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.