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In this section, you will be translating a graph into a verbal description.

A verbal description of a quadratic function using its graph mentions the following:

the location of any zeros, roots, or x-intercepts

graph of a parabola that opens down with arrows pointing to the x-intercepts at (-1,0) and (3,0)

the type of zeros, roots, or x-intercepts

Possible roots include: real, rational, irrational or imaginary numbers. Remember you must actually know the numerical value to be able to decide whether that number is rational or irrational. Study the graphs below to determine from a graph whether a parabola has real or imaginary roots.

graph of 3 parabolas one that has a vertex above the x-axis (2 imaginary roots), one that just touches the x-axis (one real double root), and one that intersects the x-axis in 2 places (2 real roots)

the location of the y-intercept

graph of a parabola showing one y-intercept

the location of the vertex
whether the parabola has a minimum or maximum

graph of 2 parabolas with one opening up (vertex is a minimum point) and one opening down (vertex is a maximum point

the location of the axis of symmetry

graph of a parabola opening up with the axis of symmetry of x= 3 and vertex of(3,-4)

where the parabola is increasing or decreasing

graph with 2 parabolas- one opening down that show it increasing to the vertex of (-5,1)then decreasing and the second one opening up that shows it decreasing to the vertex of (4,2) and then increasing

Review

When writing a verbal description for a quadratic function using its graph, identify its critical attributes and behavior which include:

the location of any zeros, roots, or x-intercepts,
the type of zeros, roots, or x-intercepts,
the location of the y-intercept,
the location of the vertex,
whether the parabola has a minimum or maximum
the location of the axis of symmetry
whether the parabola opens up or down
where the parabola is increasing or decreasing.