Answer:
B. -1
Step-by-step explanation:
If we have a parabola whose equation is:
[tex]y=ax^{2} +bx+c[/tex]
The line of symmetry is calculated as:
[tex]x=\frac{-b}{2a}[/tex]
Now, we have the equation [tex]y=ax^{2}-4x+3[/tex] and the line of symmetry is [tex]x=-2[/tex]
Where:
[tex]b=-4\\c=3[/tex]
So, we can replace [tex]b[/tex] by -4 and [tex]x[/tex] by -2 and solve for [tex]a[/tex] using the following equation as:
[tex]x=\frac{-b}{2a}\\-2=\frac{-(-4)}{2a}\\-2(2)a=4\\-4a=4\\a=-1[/tex]
It means that the equation of the parabola is equal to:
[tex]y=-1x^{2}-4x+3[/tex]
