graph each quadratic function

Question

, (a) graph each quadratic function by determining whether its graph opens up or down and by finding its vertex, axis
of symmetry, y-intercept, and x-intercepts, if any. (b) Determine the domain and the range of the function. (c) Determine where the
function is increasing and where it is decreasing.

f(x) =x^2+2x

Answer 1

Step 1:

The equation is  .

Quadratic function represents a parabola in the graph.

Compared to the quadratic function .

since then the parabola open upward.

Step 2:

Vertex is

Axis of symmetry

Axis of symmetry is

Vertex is .

Step 3:

Find the  - intercepts by substituting in .

and

Find the - intercept by substituting in .

Step 4:

Graph:

Draw the coordinate plane.

Plot the axis of symmetry, vertex and intercepts.

Connect the plotted points with a smooth curve.

Solution:

Resultants of   are shown in the figure below.

Answer 2

Step 1:

Domain of the quadratic function is all real numbers.

Domain set of is .

Domain  in interval notation

Range set of is .

Range in interval notation .

Step 6:

Graph the function .

Observe the graph,

is increasing on and decreasing on .

Solution:

Domain in interval notation and range in interval notation .

is increasing on and decreasing on .