Question

Find the axis of symmetry of the graph of the function. (5 points) f(x) = 3x2 + 12x + 9

Answer 1

Considering the definition of axis of symmetry, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

Axis of symmetry

An axis of symmetry is an imaginary reference line that, when dividing any shape into two parts, its opposite points are equidistant from each other, that is, they are symmetrical.

In other words, the axis of symmetry is a vertical line that divides the parabola into two congruent halves.

The axis of symmetry is the line perpendicular to the "x" axis that contains the vertex of the function, that is, it always passes through the vertex of the parabola. So the x-coordinate of the vertex is the equation of the axis of symmetry.

That is, in a quadratic function that has the form:

f(x)= ax² + bx + c

the axis of symmetry is a vertical line and it is defined as $x=\frac{-b}{2a}$.

Axis of symmetry of f(x) = 3x² + 12x + 9

In this case, you know:

• a= 3
• b=12
• c=9

Replacing in the definition of axis of symmetry:

$x=\frac{-12}{2x3}$

Solving:

$x=\frac{-12}{6}$

x= -2

Finally, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

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