Question

fill in the blanks so that the resulting statement is true.

the quadratic function (f(x) = a(x - h)^2 + k), (a \
eq 0), is in form. the graph of (f) is called a whose vertex is the point . the graph opens upward if and opens downward if .

Explanation:

Identify the form of the quadratic function

Using the Vertex Form of a Quadratic knowledge point

$$ f(x) = a(x-h)^2 + k,\quad a eq 0 $$

This is standardly known as the vertex form.

Identify the shape of the graph

Using the Parabola Graphing knowledge point
The graph of any quadratic function is a U-shaped curve called a parabola.

Determine the vertex coordinates

Using the Vertex Form of a Quadratic knowledge point
The vertex of the parabola represented by \(f(x) = a(x-h)^2 + k\) is located at the point \((h, k)\).

Determine the opening direction conditions

Using the Parabola Graphing knowledge point
The graph opens upward if \(a > 0\) and opens downward if \(a < 0\).

Answer:

Fill in the blanks so that the resulting statement is true.

The quadratic function \(f(x) = a(x - h)^2 + k\), \(a
eq 0\), is in <blank>vertex</blank> form. The graph of \(f\) is called a <blank>parabola</blank> whose vertex is the point <blank>\((h, k)\)</blank>. The graph opens upward if <blank>\(a > 0\)</blank> and opens downward if <blank>\(a < 0\)</blank>.