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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)

Respuesta :

ghanami
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:

The correct option is 3.

Step-by-step explanation:

The given function is

[tex]y=-2x^2+6x-1[/tex]

If a parabola is defined as

[tex]y=ax^2+bx+c[/tex]

then the axis of symmetry is

[tex]x=-\frac{b}{2a}=-\frac{6}{2(-2)}=1.5[/tex]

The vertex of the parabola is

[tex](-\frac{b}{2a},f(-\frac{b}{2a}))[/tex]

Substitute x=1.5 in the given equation.

[tex]y=-2(1.5)^2+6(1.5)-1=3.5[/tex]

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

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