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
Answers
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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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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