Question

tell whether each statement about a function of the form $f(x)=ax^2$ is always true, sometimes true, or never true.
a. the graph is a parabola that opens upward.
b. the vertex of the graph is $(0,0)$.
c. the axis of symmetry of the graph is $x = 0$.

a. the statement \the graph is a parabola that opens upward\ is about a function of the form $f(x)=ax^2$.

never true
sometimes true
always true

Explanation:

Step1: Recall the properties of \( f(x) = ax^2 \)

The graph of \( f(x)=ax^2 \) is a parabola. The direction it opens depends on the sign of \( a \). If \( a>0 \), the parabola opens upward; if \( a < 0 \), it opens downward.

Step2: Determine the truth value

Since \( a \) can be positive or negative, the statement "the graph is a parabola that opens upward" is true only when \( a>0 \), and false when \( a < 0 \). So it is sometimes true.

Answer:

sometimes true