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ALGEBRA I : SECTION 9-1 (Quadratic Graphs and Their Properties)

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1 ALGEBRA I : SECTION 9-1 (Quadratic Graphs and Their Properties)
11/20/2018 ALGEBRA I @ SECTION 9-1 : QUADRATIC GRAPHS and THEIR PROPERTIES

2 QUADRATIC FUNCTION : An equation of the form y = ax2 + bx + c
QUADRATIC FUNCTION : An equation of the form y = ax2 + bx + c. This is called STANDARD FORM. Graph y = x2 – 4x + 1 x y -1 1 2 3 4 5 What is the domain and range?

3 2) What is the name of the graph for #1?
Parabola is the name (shape) of the graph for a quadratic function. 3) What is the name of the maximum or the minimum point of a parabola? Vertex 4) What are the coordinates for the vertex for the graph of #1? (2, -3)

4 The equation for #1 was y = x2 – 4x + 1
The equation for #1 was y = x2 – 4x We can find the vertex without guessing by using the formula y = (2)2 – 4(2) + 1 = 4 – 8 + 1 = -3 5) How do you find the y-coordinate? Just “plug in” 2 for x in the original equation. Therefore, the vertex is at (2, -3)

5 AXIS OF SYMMETRY : The vertical line that contains the vertex and splits the parabola into symmetric parts. The equation is of the form A parabola is symmetric about the axis of symmetry. You can use the axis of symmetry to determine additional points on the parabola. In order to graph a parabola, find the coordinates of the vertex, find the coordinates of a second point, and use the axis of symmetry to plot a third point. Y-INTERCEPT : The point(s) where a graph crosses the y-axis. You can find the y-intercept by setting x = 0.

6 For each parabola : find the coordinates of the vertex, find the equation of the axis of symmetry, find the y-intercept, use the axis of symmetry to find a third point, and graph the parabola. 6) y = -3x2 How can we tell if the parabola opens up or down? Look at the coefficient of x2 : a < 0 : down a > 0 : up What is the domain and range?

7 What does the “+2” at the end of the equation do to the graph?
7) y = -3x2 + 2 What does the “+2” at the end of the equation do to the graph? It shifts the graph up 2 units.

8 8) Given y = ax2 + c, what are the effects of “a” and “c: on the graph?
Graphing calculator time!!!!

9 ALGEBRA I : SECTION 9-1 (Quadratic Graphs and Their Properties)
11/20/2018 a a > 0 graph opens up a < 0 graph opens down The larger a is, the narrower the graph (stretched) The smaller a is, the broader the graph (compressed) c + c The graph shifts up c units - c The graph shifts down c units

10 Examples of parabolas in everyday life.


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