Mathematics

Problem

A quadratic function has its vertex at

(2,-3)

and passes through the point

(0,5)

. a. (i) Write the function in the form

f(x)=a(x-h)^{2}+k

and determine the value of

a

. b. (ii) Express the function in the standard form

ax^{2}+bx+c

. c. (iii) State the equation of the axis of symmetry and find the value of

f(4)