Mathematics: QUADRATICS Topical Past Paper Questions

[Maximum mark: 6] Let $ f(x) = -x^{2} + 4x + 5 $ and $ g(x) = -f(x) + k $. Find the values of k so that $ g(x) = 0 $ has no real roots.

Consider the graph of the function $ f(x) = a(x + 10)^2 + 15 $, $ x \in \mathbb{R} $. (a) Write down the coordinates of the vertex. [2] (b) The graph of $ f $ has a $ y $-intercept at -20. Find $ a $. [2] (c) Point $ P(8, b) $ lies on the graph of $ f $. Find $ b $. [2]

[Maximum mark: 5] In the quadratic equation $ 7x^{2}-8x+p=0 $, $ (p\in\mathbb{Q}) $, one root is three times the other root. Find the value of p.