Question

What is f(x) = 7x2 + 42x written in vertex form?

Answer 1

Hello,

y=7x²+42x
==>y=7(x²+2*3*x+9)-63
==>y=7(x+3)²-63

Answer 2

`\boxed{\boxed{y = 7(x+3)^2-63}}`

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.