How do I find the vertex of f(x)=x^2+6x+5?

akemezaug5

akemezaug5

Answered question

2023-03-06

How do I find the vertex of f ( x ) = x 2 + 6 x + 5 ?

Answer & Explanation

Hunter Hendricks

Hunter Hendricks

Beginner2023-03-07Added 6 answers

given the parabola in standard form
x y = a x 2 + b x + c x ; a 0
then the x-coordinate of the vertex is
x x vertex = - b 2 a
f ( x ) = x 2 + 6 x + 5 is in standard form
with a = 1 , b = 6 and c = 5
x vertex = - 6 2 = - 3
substitute this value into the equation for y
y vertex = ( - 3 ) 2 + 6 ( - 3 ) + 5 = - 4
vertex = ( - 3 , - 4 )
graph{x^2+6x+5 [-10, 10, -5, 5]}
Kiara Rollins

Kiara Rollins

Beginner2023-03-08Added 6 answers

The given function:
f ( x ) = x 2 + 6 x + 5
y = x 2 + 2 ( 3 ) x + 3 2 - 3 2 + 5
y = ( x + 3 ) 2 - 4
( x + 3 ) 2 = ( y + 4 )
The following equation is a vertical parabola in its standard form:
( x - x 1 ) 2 = 4 a ( y - y 1 )
Which has vertex at
( x 1 , y 1 ) ( - 3 , - 4 )

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