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

Question

asked Jun 20, 2017 195k views

2 Answers

Sifat Ifty · Answer 1 · 2017-06-25T04:00:19+0000

Answer:

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

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.