Write the equation of the quadratic function with roots 0 and 2 and a vertex at (1, 5).Enter your answer as a function beginning with f(x). Do not write any spaces. Use ^ to type exponents. Leave your answer in the form:f(x)=(a)(x^2+bx+c) Sample answer:f(x)=(-1/8)(x^2+5x-12)

Question

Write the equation of the quadratic function with roots 0 and 2 and a vertex at (1, 5).Enter your answer as a function beginning with f(x).  Do not write any spaces.  Use ^ to type exponents.  Leave your answer in the form:f(x)=(a)(x^2+bx+c) Sample answer:f(x)=(-1/8)(x^2+5x-12)

anonymous · Answer

since the roots are given at x=0 and x=2, the factored quadratic will look like:
$\large y=a(x-0)(x-2)=a(x^2-2x) $
$\large y=a(x^2-2x) $
now you need to find "a"....  
since you know the vertex passes through (1, 5), plug this into that last equation and solve for a....

anonymous · Answer

so 1 is x and y is 5 so would it look like this 5=a(1^2-2(1) is that correct

anonymous · Answer

yes....

anonymous · Answer

so a = ????

anonymous · Answer

5

anonymous · Answer

good so now your can you get the equation in standard form y=ax^2 + bx + c   ???

anonymous · Answer

i have no clue.. I got y=5 (1^2 then where does the b and c come in

anonymous · Answer

ohh...
is this the way they want the answer:  $\large f(x)=(a)(x^2+bx+c) $   ?????

or is it:  $\large f(x)=ax^2+bx+c $  ????

anonymous · Answer

the first one the f(x)=(a)(x^2+bx+c)

anonymous · Answer

the first one so:
$\large f(x)=(-5)(x^2-2x) $  is your answer..
double check that a=-5 not 5... is that right???

anonymous · Answer

i think so

anonymous · Answer

then ur done....