smithcaleb643
contestada

Tell whether each statement about a function of the form f(x) = ax2 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​

Respuesta :

Using quadratic function concepts, it is found that the correct answer regarding each statement is given as follows:

a. Sometimes true.

b. True.

c. True.

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

The axis of symmetry is [tex]x = x_v[/tex].

Considering the coefficient a, we have that:

  • If a < 0, the vertex is a maximum point.
  • If a > 0, the vertex is a minimum point.

In this problem, the coefficients are a, b = 0, c = 0.

If a > 0, it opens upward, a < 0 downwards, hence item a is sometimes true.

As for items b and c, we have that:

[tex]x_v = -\frac{b}{2a} = -\frac{0}{2a} = 0[/tex]

Hence they are true.

More can be learned about quadratic function concepts at https://brainly.com/question/24737967