Question

find the y-intercept, the axis of symmetry, and the vertex of the graph of the function.\\( f(x) = -3x^2 + 6x - 2 \\)\\( \\)\\( \\)the y-intercept is \\( (0, -2) \\). (type an ordered pair.)\\( \\)the axis of symmetry is \\( \square \\). (simplify your answer. type an equation.)

Explanation:

Step1: Recall the formula for axis of symmetry

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

Step2: Identify \( a \) and \( b \) from the function

In the function \( f(x) = -3x^2 + 6x - 2 \), we have \( a = -3 \) and \( b = 6 \).

Step3: Substitute \( a \) and \( b \) into the formula

Substitute \( a = -3 \) and \( b = 6 \) into \( x = -\frac{b}{2a} \):
\[
x = -\frac{6}{2\times(-3)}
\]

Step4: Simplify the expression

First, calculate the denominator: \( 2\times(-3)=-6 \). Then, \( -\frac{6}{-6} = 1 \). So the axis of symmetry is \( x = 1 \).

Answer:

The axis of symmetry is \( x = 1 \)