Find quadratic from roots/properties

A question is this type if and only if it requires finding the coefficients of a quadratic given information about its roots, vertex, or specific point values.

2 questions · Moderate -0.8

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OCR C1 2008 January Q3
4 marks Moderate -0.8
3 Given that \(3 x ^ { 2 } + b x + 10 = a ( x + 3 ) ^ { 2 } + c\) for all values of \(x\), find the values of the constants \(a , b\) and \(c\).
CAIE P1 2011 June Q3
5 marks Moderate -0.8
The equation \(x^2 + px + q = 0\), where \(p\) and \(q\) are constants, has roots \(-3\) and \(5\).
  1. Find the values of \(p\) and \(q\). [2]
  2. Using these values of \(p\) and \(q\), find the value of the constant \(r\) for which the equation \(x^2 + px + q + r = 0\) has equal roots. [3]