A quadratic function has its vertex at and passes through the point .

MATHEMATICS · Multi-part · AoPS · Mathematics · Graphing Quadratics · Graphing Quadratics

Problem

A quadratic function has its vertex at

(2,-3)

and passes through the point

(0,5)

. (i) Write the function in the form

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

and determine the value of

a

. (ii) Express the function in the standard form

ax^{2}+bx+c

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

f(4)