Question

analyzing the graph of a quadratic function
the function ( f(x) = -0.3(x - 5)^2 + 5 ) is graphed. what are some of its key features? check all that apply
( square ) the axis of symmetry is ( x = 5 ).
( square ) the domain is ( {x | x \text{ is a real number}} ).
( square ) the function is increasing over ( (-infty, 5) ).
( square ) the minimum is ( (5, 5) ).
( square ) the range is ( {y | y geq 5} ).

Explanation:

Step1: Identify axis of symmetry

For quadratic $f(x)=a(x-h)^2+k$, axis is $x=h$. Here $h=5$, so $x=5$.

Step2: Determine domain

Quadratic functions accept all real $x$, so domain is all real numbers.

Step3: Analyze increasing interval

$a=-0.3<0$, parabola opens down. It increases left of vertex: $(-\infty,5)$.

Step4: Check min/max

Opens down, so vertex $(5,5)$ is a maximum, not minimum.

Step5: Find range

Since vertex is maximum $y=5$, range is $\{y \mid y \leq 5\}$, not $y\geq5$.

Answer:

• The axis of symmetry is $x = 5$
• The domain is $\{x \mid x \text{ is a real number}\}$
• The function is increasing over $(-\infty, 5)$