Question

Help please
Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = –2x^2 +6x – 1.

A) x = 3; vertex: (3, 35)
B) x = –1.5; vertex: (–1.5, – 14.5)
C) x = –1.5; vertex: (–1.5, –5.5)
D) x = 1.5; vertex: (1.5, 3.5)

Answer 1

from the equation, after simplifying u will get
\[(x-\frac{ 3 }{ 2 })^{2} = -\frac{ y }{ 2 }+\frac{ 7 }{ 4 }\]

Answer 2

now can u solve

Answer 3

this question is same just like we did on the previous thred \[\huge\rm \frac{ -b }{ 2a }\]
use this formula to find x-coordinate of the vertex

Answer 4

IN the general quadratic\[y=ax^2 + bx + c\]the axis of symmetry is the vertical lineline\[x=-\frac{ b }{ 2a }\]Yhis also gives the x-coordinate of the vertex. Plug this value of x back into the function to get the y-coordinate of the vertex.

Answer 5

and then replace x by its value into the equation to find y-coordinate
axis of symmetry = x coordinate of the vertex

Answer 6

can we go over this step by step.. still confused
So I replace b with -2 and a with 6? @Nnesha

Answer 7

no \[\huge\rm Ax^2+Bx+C=0\]
B is middle term
A is leading coefficient

Answer 8

Oh actually the opposite I mean.. -2 -> a and 6 -> b

Answer 9

yes!!

Answer 10

substitute b and a by their values into the formula

Answer 11

-(6)/2(-2)

Answer 12

yes!

Answer 13

so now we divide by -2?

Answer 14

there is 2(-2) you can multiply them first or reduce the fraction

Answer 15

-(6)/-4

Answer 16

yes right :=)

Answer 17

can you reduce the fraction -6/-4 = ?

Answer 18

so now we simplify

Answer 19

yes divide by 2 or -2

Answer 20

okay so -6/-4 = ?

Answer 21

3/2

Answer 22

and then 3/2 = 1.5 right?

Answer 23

yes right

Answer 24

now find y-coordinate of the vertex

Answer 25

y = -2(1.5)^2 + 6(1.5) - 1?

Answer 26

yes

Answer 27

= 3.5

Answer 28

the answer is D

Answer 29

D) x = 1.5; vertex: (1.5, 3.5)

Answer 30

yes right!

Answer 31

thanks

Answer 32

my pleasure