Answer :
Answer:
Axis of symmetry: [tex]x=1.5[/tex]
Vertex is at (1.5, 3.5).
Step-by-step explanation:
Given:
The equation of the parabola is given as:
[tex]y=-2x^2+6x-1[/tex]
The standard form of a parabola is given as:
[tex]y=ax^2+bx+c[/tex]
On comparing the given equation with the standard form, we get:
[tex]a=-2,b=6,\ and\ c=-1[/tex]
We know that, for a parabola, the axis of symmetry is given as:
[tex]x=-\frac{b}{2a}\\x=-\frac{6}{2(-2)}\\x=-\frac{6}{-4}=\frac{3}{2}\\x=1.5[/tex]
Therefore, the equation of the axis of symmetry is [tex]x=1.5[/tex]
The vertex of a parabola is given as [tex](h,k)[/tex] where:
[tex]h=-\frac{b}{2a}\\h=-\frac{6}{-4}=1.5\\\\k=f(h)=f(1.5)\\k=-2(1.5)^2+6(1.5)-1\\k=-2(2.25)+9-1\\k=-4.5+8=3.5[/tex]
Therefore, the vertex of the given parabola is at the point (1.5, 3.5)