Question

what is the axis of symmetry of ( h(x) = -2x^2 + 12x - 3 )?
( circ x = -15 )
( circ x = -3 )
( circ x = 3 )
( circ x = 15 )

Explanation:

Step1: Recall axis of symmetry formula

For a quadratic function \( h(x) = ax^2 + bx + c \), the axis of symmetry is given by \( x = -\frac{b}{2a} \).

Step2: Identify \( a \) and \( b \)

In \( h(x) = -2x^2 + 12x - 3 \), we have \( a = -2 \) and \( b = 12 \).

Step3: Calculate the axis of symmetry

Substitute \( a \) and \( b \) into the formula: \( x = -\frac{12}{2\times(-2)} \).
Simplify the expression: \( x = -\frac{12}{-4} = 3 \).

Answer:

\( x = 3 \) (corresponding to the option "x = 3")