Answer:
\(\boxed{\boxed{y = 7(x+3)^2-63}}\)
Step-by-step explanation:
The general vertex form of parabola is,
\(y=a(x-h)+k\)
where,
(h, k) is the vertex of the parabola.
The given function is,
\(\Rightarrow f(x) = 7x^2 + 42x\)
\(\Rightarrow y = 7x^2 + 42x\)
\(\Rightarrow y = 7(x^2 + 6x)\)
\(\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3)\)
\(\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3-3^2)\)
\(\Rightarrow y = 7(x^2 + 2\cdot x\cdot 3+3^3)-7\cdot 3^2\)
\(\Rightarrow y = 7(x+3)^2-7\cdot 9\)
\(\Rightarrow y = 7(x+3)^2-63\)
This is vertex form the given function.
