Question

consider the function shown.
$f(x)=x^2+6x+5$
the function is stated in general form.
what can you conclude about the graph of
a quadratic function in general form?
identify the shape of the graph:
enter the equation for the axis of symmetry, and sketch it on the
graph.

Explanation:

Step1: Determine parabola direction

For quadratic $f(x)=ax^2+bx+c$, $a=1>0$, so opens upward (U-shape).

Step2: Calculate axis of symmetry

Use formula $x=-\frac{b}{2a}$. Here $a=1, b=6$.
$x=-\frac{6}{2\times1}=-3$

Answer:

• Shape of the graph: Upward-opening parabola (U-shape)
• Equation for the axis of symmetry: $x=-3$ (the vertical dashed line at $x=-3$ shown in the graph is this axis)