What is the equation of the quadratic function with a vertex at (2,-25), and an x-intercept at(7,0)
Accepted Solution
A:
Let start with some basic theory of quadraticsIf f(x)=ax2+bx+c a,b,c ∈R a≠0 f(x)=ax2+bx+c a,b,c ∈R a≠0 has 2 2 roots r1 r1 and r2 r2 than it can take the form f(x)=a(x−r1)(x−r2).f(x)=a(x−r1)(x−r2).The maximum or minimum value of f(x) f(x) is M=−(b2–4ac)4a M=−(b2–4ac)4aIf a>0 a>0 then M M is the minimum value and if a<0 a<0 then M M is the maximum value. Lets go now to the questionSince 2 2 and 7 7 are the roots our function will be f(x)=a(x−2)(x−7), a∈R f(x)=a(x−2)(x−7), a∈Rso f(x)=a(x2