Answer:
value of a is 1.
Step-by-step explanation:
A quadratic equation \(y=ax^2+bx+c\) ....[1] where a, b and c are the coefficient.
then the axis of symmetry is given by:
\(x = -\frac{b}{2a}\) .....[2]
As per the statement:
The line of symmetry for the quadratic equation \(y = ax^2-2x -3\) is x = 1.
On comparing given quadratic equation with [1] we have;
b = -2
then;
Substitute x = 1 in [2] we have;
\(1= -\frac{-2}{2a}\)
Simplify:
\(1 = \frac{1}{a}\)
⇒\(a = 1\)
Therefore, the value of a is 1.