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© Boardworks Ltd of 5 Graphs of quadratic functions
© Boardworks Ltd of 5 Plotting graphs of quadratic functions Plot the graph of y = x 2 – 4 x + 2 for –1 < x < 5. We can plot the graph of a quadratic function using a table of values. For example: x x2x2 – 4 x + 2 y = x 2 – 4 x + 2 – – 4– 8– 12– 16– –1–2–127 y = ax 2 + bx + c (where a 0) A quadratic function in x can be written in the form:
© Boardworks Ltd of 5 x 1 01– y 2 Plotting graphs of quadratic functions x y = x 2 – 4 x + 2 – –2–127 The points given in the table are plotted … … and the points are then joined together with a smooth curve. The shape of this curve is called a parabola. It is characteristic of a quadratic function.
© Boardworks Ltd of 5 Parabolas When the coefficient of x 2 is positive the vertex is a minimum point and the graph is -shaped. When the coefficient of x 2 is negative the vertex is a maximum point and the graph is -shaped. Parabolas have a vertical axis of symmetry … …and a turning point called the vertex.
© Boardworks Ltd of 5 Graphs of the form y = ax 2 + bx + c
Quadratic Function has the form y=ax 2 +bx+c where a cannot be 0 and the graph is a “U-shaped” called a parabola. --ax 2 : quadratic term --bx:
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5.2 Properties of Parabolas. y = ax 2 + bx + c Standard Form c is the y-intercept. If b = 0 then y = ax 2 + c Axis of symmetry: x = 0 Vertex (0, c)
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Copyright © 2013, 2009, 2005 Pearson Education, Inc. Section 8.1 Quadratic Functions and Their Graphs.
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