Question

diagaram 11shows two curves y=4(x-3)^2 + 2n and y=x^2-2x+mx+8 which intersect the axis at point p and q.

a) find the value of m
b) if a and b are the roots 4(x-3)^2+m=k and a^2+b^2=4 fins k

Answer 1

As both parabolas have the same roots p and q, they both have a minimum that occurs at x midway between the 2 roots. For a parabola in the standard form
\[ ax^2+bx+c=0\]
this min occurs at x= -b/(2a)

To answer (a), put both parabolas into the standard form and equate their -b/(2a) values
To answer (b)
put 4(x-a)(x-b)=0 and 4(x-3)^2+m=k in standard form (using m's value from step (a))
equate corresponding coefficients. Notice that you must square the coefficients of the x term to take advantage of the given relation a^2 + b^2 =4