Question

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function y = –2x2 +6x – 1.

x = 3; vertex: (3, 35)]

x = –1.5; vertex: (–1.5, – 14.5)

x = 1.5; vertex: (1.5, 3.5)

x = –1.5; vertex: (–1.5, –5.5)

Answer 1

hello:
y = –2x2 +6x – 1.
y = -2(x²-3x)-1
y= -2(x²-2(3/2)x+(3/2)² -(3/2)²) -1
y = -(x-3/2)²+9/2-1
y = - (x-3/2)² +7/2
answer : x = 1.5; vertex: (1.5, 3.5) because : 3/2=1.5 and : 7/2 = 3.5

Answer 2

The correct option is 3.

Explanation:

The given function is

`y=-2x^2+6x-1`

If a parabola is defined as

`y=ax^2+bx+c`

then the axis of symmetry is

`x=-(b)/(2a)=-(6)/(2(-2))=1.5`

The vertex of the parabola is

`(-(b)/(2a),f(-(b)/(2a)))`

Substitute x=1.5 in the given equation.

`y=-2(1.5)^2+6(1.5)-1=3.5`

Therefore the axis of symmetry is x = 1.5 and vertex is (1.5, 3.5). Option 3 is correct.