Question

find the y - intercept, the axis of symmetry, and the vertex of the graph of the function.
$f(x)=0.6x^{2}-3.6x$
the y - intercept is (0,0). (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 of a quadratic function

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

Step2: Identify a and b from the given function

In the function \( f(x) = 0.6x^2 - 3.6x \), we have \( a = 0.6 \) and \( b = -3.6 \).

Step3: Substitute a and b into the formula

Substitute \( a = 0.6 \) and \( b = -3.6 \) into \( x = -\frac{b}{2a} \):
\[
x = -\frac{-3.6}{2 \times 0.6}
\]

Step4: Simplify the expression

First, simplify the numerator: \( -(-3.6) = 3.6 \). Then, simplify the denominator: \( 2 \times 0.6 = 1.2 \). Now, divide: \( \frac{3.6}{1.2} = 3 \). So, \( x = 3 \).

Answer:

The axis of symmetry is \( x = 3 \)