SOLUTION: Question 1 (a) Write the function f(x) = 2x ^ 2 - 7x - 10 where x ∈ R, in the form a * (x + h) ^ 2 + k_{i} where a, h, and k \in Qb) Hence, write the minimum point of f

Algebra ->  Functions -> SOLUTION: Question 1 (a) Write the function f(x) = 2x ^ 2 - 7x - 10 where x ∈ R, in the form a * (x + h) ^ 2 + k_{i} where a, h, and k \in Qb) Hence, write the minimum point of f       Log On


   

Question 1208807: Question 1
(a) Write the function f(x) = 2x ^ 2 - 7x - 10 where x ∈ R, in the form a * (x + h) ^ 2 + k_{i} where a, h, and k \in
Qb) Hence, write the minimum point of f
(c) (i) Explain why / must have two real roots.
(ii) Write the roots of f(x) = 0 in the form p plus/minus sqrt(q) where p and q \in \mathbb{Q}
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2%28x%5E2-7x%2F2-5%29
2%28x%5E2-7x%2F2%2B%287%2F4%29%5E2-%287%2F4%29%5E2-5%29
2%28%28x-7%2F4%29%5E2-49%2F16-5%29
2%28x-7%2F4%29%5E2-49%2F8-10
2%28x-7%2F4%29%5E2-129%2F8
highlight%282%28x-7%2F4%29%5E2-16%261%2F8%29
The vertex here will be the lowest point of the graph
which is at (1&3/4, -16&1/8).
h=7%2F4 and k=-16%261%2F8.

If solve f(x) equated at 0, then you find the roots.
2%28x-7%2F4%29%5E2-16%261%2F8=0.

2%28x-7%2F4%29%5E2-129%2F8=0
2%28x-7%2F4%29%5E2=129%2F8
%28x-7%2F4%29%5E2=129%2F16
x-7%2F4=0%2B-+sqrt%28129%29%2F4
highlight%28x=7%2F4%2B-+sqrt%28129%29%2F4%29 the roots