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2.3 Quadratic 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.
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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.
Graphs of a quadratic function f(x) = ax2 + bx + c Vertex is highest point Axis of symmetry Axis of symmetry a> 0 a< 0 Opens up Opens down Vertex is lowest point
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.
(2,4) (0,0)
(0,0) (2, -12)
(2, 0) (4, -12)
Vertex (2, 13)
Determine whether the graph opens up or down. Find its vertex, axis of symmetry, y-intercept, x-intercept. x-coordinate of vertex: y-coordinate of vertex: Axis of symmetry:
(0, 5) (-5.55, 0) (-0.45, 0) Vertex: (-3, -13)