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Properties of Quadratic Functions in Standard Form 5-1
SWBAT Define, identify, and graph quadratic functions. Identify and use maximums and minimums of quadratic functions to solve problems. Holt Algebra 2
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Vocabulary Quadratic Function: An equation with a degree of 2.
Standard Form: y = ax2 + bx + c Parabola: A quadratic graph that has a U shape Vertex: The lowest or highest point of the graph Axis of Symmetry: The line passing through the vertex that divides thee parabola in half
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This shows that parabolas are symmetric curves
This shows that parabolas are symmetric curves. The axis of symmetry is the line through the vertex of a parabola that divides the parabola into two congruent halves.
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These properties can be generalized to help you graph quadratic functions.
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A is positive A is negative
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Graphing a Quadratic Function
Step 1: Find the x-coordinate of the vertex Step 2: Make a table. Use 2 values to the left & right of the vertex Step 3: Plot the points and make a curve similar to a U Step 4: Analyze parts of the graph.
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The minimum (or maximum) value is the y-value at the vertex
The minimum (or maximum) value is the y-value at the vertex. It is not the ordered pair that represents the vertex. Caution!
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Graph: f(x) = x2 – 4x + 4 x Work y
Standard Form: ___________ a =___ b =___ c = ___ Vertex: _____ D: _______ AOS: _____ R: _______ Min: _____ Max: _____ Zeros: _____ x Work y
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Homework: Reading Strategies & Extra Practice Worksheet.
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