Let and consider the general quadratic function .

MATHEMATICS · Multi-part · CBSE · Mathematics · Quadratic Equations · Quadratic Equations

Problem

Let

a\neq 0

and consider the general quadratic function

f(x)=ax^{2}+bx+c

. (i) Rewrite

f(x)

in the completed–square form. (ii) Using the result of part (i), show that the extremum value of

f(x)

-\dfrac{b^{2}-4ac}{4a}

and state whether this value is a maximum or a minimum according to the sign of

a

. (iii) Verify your result from part (ii) for the specific quadratic

h(x)=-3x^{2}+12x+7