The equation of a parabola is given. y=34x2−6x+15 What are the coordinates of the vertex of the parabola? Enter your answer in the boxes. ( , )

Question

asked Feb 14, 2020 109k views

2 Answers

Cchampion · Answer 1 · 2020-02-20T14:26:53+0000

ANSWER

( (3)/(34) , (501)/(34) )

Step-by-step explanation

The given parabola has equation;

$y = 34 {x}^(2) - 6x + 15$

Comparing this equation to

$y = a{x}^(2) + bx + c$

we have

a=34, b=-6 and c=15

The x-coordinate of the vertex is given by:

x = ( - b)/(2a)

x = ( - - 6)/(2(34))

x = ( 6)/(2(34))

x = ( 3)/(34)

The y-coordinates of the vertex is obtained by substituting the x-value of the vertex into the equation:

$y = 34( { (3)/(34) })^(2) - 6( (3)/(34)) + 15$

y = { (9)/(34) } - (18)/(34)+ 15

y = (501)/(34)

The vertex is

( (3)/(34) , (501)/(34) )