2.3 Quadratic Functions. A quadratic function is a function of the form:
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Transcript of 2.3 Quadratic Functions. A quadratic function is a function of the form:
2.3Quadratic Functions
A quadratic function is a function of the form:
Properties of the Graph of a Quadratic Function
Parabola opens up if a > 0; the vertex is a minimum point.Parabola opens down if a < 0; the vertex is a maximum point.
a > 0Opens up
Vertex is lowest point
Axis of symmetry
Graphs of a quadratic function f(x) = ax2 + bx + c
a < 0Opens down
Vertex is highest point
Axis of symmetry
Steps for Graphing a Quadratic Function by Hand
• Determine the vertex.• Determine the axis of symmetry.• Determine the y-intercept, f(0).• Determine how many x-intercepts the graph has. • If there are no x-intercepts determine another
point from the y-intercept using the axis of symmetry.
• Graph.
Without graphing, locate the vertex and find the axis of symmetry of the following parabola. Does it open up or down?
Vertex:
Since -3 < 0 the parabola opens down.
Finding the vertex by completing the square:
10 0 10
15
15
(0,0)
(2,4)
y x= 2
10 0 10
15
15
(0,0)
(2, -12)
10 0 10
15
15
(2, 0)
(4, -12)
10 0 10
15
15
(2, 13)Vertex
Determine whether the graph opens up or down.Find its vertex, axis of symmetry, y-intercept, x-intercept.
x-coordinate of vertex:
Axis of symmetry:
y-coordinate of vertex:
There are two x-intercepts:
5 0
10
10
Vertex: (-3, -13)
(-5.55, 0) (-0.45, 0)
(0, 5)