• are symmetric about a central line called the axis of symmetry

• ​the axis of symmetry intersects the parabola at the vertex

​Parabolas

• a ≠ 0

• Parent function: f(x) = x²

• type of graph: parabola (nonlinear)​

​f(x) = ax² + bx + c

Characteristics of Quadratic Functions

Some text here about the topic of discussion

• the graph opens downward

• the highest point is called the maximum

• range: all real numbers less than or equal to the maximum​

​when a < 0

• the graph opens upward

• the lowest point is called the minimum

• range: all real numbers greater than or equal to the minimum​

​when a > 0

Characteristics of Quadratic Functions

The maximum or minimum is the vertex and the axis of symmetry cuts through the vertex.

Vertex:

​

Axis of sym:

​

y-int:​

​

​domain:

​

range:​​

Identify characteristics from graphs

​

Plug in the axis of symmetry for x

​Vertex

Plug in a and b and solve.

Axis of Symmetry

y = 2x²+4x-3

Maximum or Minimum?

a < 1 a > 1​