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Published byCollin Lester Modified over 9 years ago
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Quadratic Functions Solving by Graphing
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Quadratic Function Standard Form: f(x) = ax 2 + bx + c
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Solving Quadratic Equations To solve, we need to find the value of x when y = 0 or f(x) = 0. Located at: x-intercepts Referred to as: solutions, zeros, or roots.
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The number of real solutions is at most two. Quadratic Solutions No Real SolutionsOne SolutionTwo Solutions
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Example f(x) = x 2 - 4 Identifying Solutions Solutions are x = -2 and x = 2.
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Quadratic Function (y = ax 2 + bx + c) Each will have a vertex: either a maximum or minimum point. Line of symmetry: divides the graph in two halves
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Quadratic Functions The graph of a quadratic function is a: If the parabola opens up, the lowest point is called the vertex (minimum). If the parabola opens down, the vertex is the highest point (maximum). Vertex parabola
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y x Axis of Symmetry Parabolas are symmetric. Axis of symmetry The Axis of symmetry ALWAYS passes through the vertex.
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Parent Function: f(x) = x 2 a = 1, b = 0, c = 0 Minimum point (0,0) Axis of symmetry x=0 y=x 2
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What happen if we change the value of a and c ? Y=4x 2 y=-3x 2 y=4x 2 +3 y=-4x 2 -2
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Conclusion (y = ax 2 +bx+c) When a is positiveConcave (opens up) When a is negative,Convex (opens down) When c is positive, Moves Up When c is negative,Moves Down
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y = ax 2 + bx + c a > 0 a < 0
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Finding the Axis of Symmetry When a quadratic function is in standard form the equation of the Axis of symmetry is y = ax 2 + bx + c,
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STEP 1: Find the Axis of symmetry STEP 2: Make a table of 3 points Axis of Symmetry: Vertex: Min or Max? Roots: Y-intercept:
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Axis of Symmetry: Vertex: Min or Max? Roots: Y-intercept:
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