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