Algebra 2 Notes (9-4)

Graphs of Quadratic Functions

Words to Know

• parabola-

• quadratic function-

• vertex of a parabola-

Words to Know

• parabola- graph of a quadratic function

• quadratic function- a function whose equation is in the form of _____________

where ____

• vertex of a parabola- the point where the graph crosses the line of symmetry

f(x) ax2 bx ca 0

Graphs of • Vertex of graphs will always be (0, 0)

• Line of symmetry will always be on the y-axis which means ____

• Example 1– Graph the equation – What is the line of symmetry?– What is the vertex?

f(x) ax2

x 0

f(x) 2x2

Example 1 Solution• The line of symmetry is ____

• The vertex is ____

• The graph of the function is:

x 0(0, 0)

line of symmetry vertex (0, 0)

• Vertex of graphs will always be , where h can be any real number

• Line of symmetry will be

• Example 2– Graph the equation – What is the line of symmetry?– What is the vertex?– What is the shift of the graph from the

equation ? (Shifting will be more in-depth in Chapter 9-5)

Graphs of f(x) a(x h)2(h, 0)

x h

f(x) (x 2)2

f(x) x2

Example 2 Solution• The line of symmetry is ____

• The vertex is ____

• The graph of the function is:

x 2(2, 0)

line of symmetry vertex (2, 0)

Example 2 Solution (cont.)• The shift of the graph from the origin is

_________________two units to the right.

f(x) x2

f(x) (x 2)2

Distinguishing Between • If the equation of the graph is , then

the following statements are true.– The line of symmetry will be– The vertex will be– The graph will always move to the left.

• If the equation of the graph is , then the following statements are true.– The line of symmetry will be– The vertex will be– The graph will always move to the right.

f(x) (xh)2f(x) (x h)2

x h( h, 0)

f(x) (x h)2

x h(h, 0)

Homework

• Pg.402 #1-25– For the first 4 problems you don’t need to

graph, just determine whether it is above or below the x-axis

– For problems #19-24, test out a point and see where the inequality makes sense.