Find the value of k if the equation 𝑘 2 𝑥 2 + 2(𝑘 + 1)𝑥 + 4 has equal roots
A quadratic function has roots of -2 and -1. It also contains the point (-3, 8). Evaluate the function in
the form 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 𝑐 where 𝑎, 𝑏, 𝑐 ∈ 𝑍
The function 𝑓(𝑥) = 2𝑥 2 + 8𝑥 − 4 can be expressed as 𝑎(𝑥 + 𝑏)2 + 𝑐,where 𝑎, 𝑏, 𝑐 ∈ 𝑍
(i)
(ii)
(iii)
(iv)
(v)
Find the values of 𝑎, 𝑏 and 𝑐.
Hence, find the co-ordinates of the local minimum of the curve.
Solve the equation 𝑓(𝑥), writing your answers in surd form.
Where does the graph cut the y-axis?
Draw a rough sketch of f(x) on the graph paper given
Factorise the following quadratics: (i) 4𝑥 2 + 31𝑥 + 21 (ii) 5𝑥 2 − 42𝑥 − 27
Write down a quadratic equation that has roots of -1 and 4 in the form of 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 where
𝑎, 𝑏, 𝑐 ∈ 𝑍 .
A quadratic function has roots of 4 and -3. It also contains the point (0, -24). Write down the
function in the form of 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 where 𝑎, 𝑏, 𝑐 ∈ 𝑍 .
The function 𝑓(𝑥) = 2𝑥 2 + 8𝑥 − 2 can be expressed as 𝑎(𝑥 + 𝑏)2 + 𝑐 where 𝑎, 𝑏, 𝑐 ∈ 𝑍
(i)
(ii)
(iii)
Using the method of completing the square, find the values of a,b and c.
Hence, find the co-ordinates of the local minimum of the curve.
Solve the equation f(x) = 0, writing your answer in surd form