Question

What is f(x) = 7x2 + 42x written in vertex form?
f(x) = 7(x + 6)2 – 6
f(x) = 7(x + 6)2 – 42
f(x) = 7(x + 3)2 – 9
f(x) = 7(x + 3)2 – 63

Answer 1

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

A) f(x) = 7(x + 6)2 – 6

B) f(x) = 7(x + 6)2 – 42

C) f(x) = 7(x + 3)2 – 9

D) f(x) = 7(x + 3)2 – 63

Solution :-

we know that, the vertex form of a quadratic function is given by :-

• f(x) = a(x - h)² + k

→ f(x) = 7x² + 42x

Let f(x) is equal to y ,

→ y = 7x² + 42x

adding 63 both sides ,

→ y + 63 = 7x² + 42x + 63

→ y + 63 = 7(x² + 6x + 9)

→ y + 63 = 7(x + 3)²

→ y = 7(x + 3)² - 63

therefore,

→ f(x) = 7(x + 3)² - 63 (D) (Ans.)

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Answer 2

Given : f(x) = 7x² + 42x

To Find : vertex form  

f(x) = 7(x + 6)² – 6

f(x) = 7(x + 6)² – 42

f(x) = 7(x + 3)² – 9

f(x) = 7(x + 3)² – 63

Solution:

f(x) = 7x² + 42x

=>  f(x) = 7(x² + 6x)

=>    f(x) = 7(x² + 6x  + 9  - 9 )

=>  f(x) = 7(x² + 6x  + 9  ) - 63

=> f(x) = 7(x + 3  )² - 63

f(x) = 7(x + 3  )² - 63  is the vertex  form  of  f(x) = 7x² + 42x

And ( - 3 , - 63 ) is the vertex

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