How does the value of a affect the graphs?

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Presentation transcript:

How does the value of a affect the graphs? Visual Warm up How does the value of a affect the graphs?

How does the value of b affect the graph? Visual warm up How does the value of b affect the graph?

How does the value of c affect the graph? Visual warm up How does the value of c affect the graph?

9.3 Graphing Quadratic Functions To graph quadratic equations on a coordinate plane. Objective: VOCABULARY Every quadratic function has a U-shaped graph called a parabola. The vertex of a parabola is the lowest point (minimum) of a parabola that opens up and the highest point (maximum) of a parabola that opens down. The axis of symmetry of a parabola is the vertical line passing through the vertex.

Parts of a parabola Vertex Axis of Symmetry y-intercept x-intercept (root) X-intercept (root) Vertex

If a is positive, the parabola opens up. GRAPH OF A QUADRATIC FUNCTION The graph of y = ax2 + bx + c is a parabola. If a is positive, the parabola opens up. If a is negative, the parabola opens down. The vertex has an x-coordinate of –b . 2a The axis of symmetry is the vertical line x = –b . 2a The y-intercept is c.

GRAPHING A QUADRATIC FUNCTION Step 1: Find the x-coordinate of the vertex. Step 2: Make a table of values, using x-values to the left and right of the vertex. Step 3: Plot the points and connect them with a smooth curve to form a parabola.

Graph x y a = 1 b = –2 c = –3 -2 -1 1 2 3 4 5 -3 -4 -3 5 The x-coordinate of the vertex is Make a table using 1 in the middle, and points to the left and right. Complete the table The axis of symmetry is the line x = 1 The vertex is (1,-4) x y -2 -1 1 2 3 4 5 -3 -4 -3 5