Answer:
Expert-Verified Answer
No one rated this answer yet — why not be the first?
psm22415
Ace
9.7K answers
19.5M people helped
The vertex of the parabolic equation is ( 2 , -5 )
What is a Parabola?
A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the parabolic equation be represented as g ( x )
Now , the value of g ( x ) ois
g ( x ) = 3x² - 12x + 7
The equation is of the form y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
On solving the equation in the form y = a ( x - h )² + k , we get
y = 3 ( x² - 4x ) + 7
y = 3 [ ( x - 2 )² - 4 ] + 7
y = 3 [ ( x - 2 )² ] - 12 + 7
On further simplification , we get
y = 3 ( x - 2 )² - 5
Therefore , the vertex of the parabola is ( 2 , -5 )
Explanation: