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Exam-Style Question on FunctionsA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 68. This question is similar to one that appeared on an IB Standard paper in 2014. The use of a calculator is not allowed.
Let \(f(x)=5x^2-20x+k\). The equation \(f(x)=0\) has two equal roots.
(a) Write down the value of the discriminant.
(b) Hence, show that \(k=20\).
The graph of \(f\) has its vertex on the x-axis.
(c) Write down the solution of \(f(x)=0\).
(d) Find the coordinates of the vertex of the graph of \(f\).
The function can be written in the form \(f(x)=a(x-h)^2+j\).
(e) Find the value of \(a\).
(f) Find the value of \(h\).
(g) Find the value of \(j\).
(h) The graph of a function \(g\) is obtained from the graph of \(f\) by a reflection in the x-axis, followed by a translation by the vector \(\begin{pmatrix} 0 \\ 3 \\ \end{pmatrix} \). Find \(g\), giving your answer in the form \(g(x)=Ax^2+Bx+C\).
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