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Factor and Solve Quadratic Equations Ms. Nong

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What is in this unit? Graphing the Quadratic Equation Identify the vertex and intercept(s) for a parabola Solve by taking SquareRoot & Squaring Solve by using the Quadratic Formula Solve by Completing the Square Factor & Solve Trinomials (split the middle) Factor & Solve DOTS: difference of two square Factor GCF (greatest common factors) Factor by Grouping

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The ROOTS (or solutions) of a polynomial are its x- intercepts Recall: The x-intercepts occur where y = 0. Roots ~ X-Intercepts ~ Zeros means the same

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The number of real solutions is at most two. Solving a Quadratic No solutions One solution X = 3 Two solutions X= -2 or X = 2 The x-intercepts (when y = 0) of a quadratic function are the solutions to the related quadratic equation.

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Vertex (h,k) Maximum point if the parabola is up-side- down Minimum point is when the Parabola is UP a>0a<0

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All parts labeled

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Can you answer these questions? How many Roots? Where is the Vertex? (Maximum or minimum) What is the Y-Intercepts?

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What is in this unit? Graph the quadratic equations (QE) Solve by taking SquareRoot & Squaring Solve by using the Quadratic Formula Solve by Completing the Square Factor & Solve Trinomials (split the middle) Factor & Solve DOTS: difference of two square Factor GCF (greatest common factors) Factor by Grouping

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Find the Axis of symmetry for y = 3x 2 – 18x + 7 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, This is best read as … ‘the opposite of b divided by the quantity of 2 times a.’ The Axis of symmetry is x = 3. a = 3 b = -18

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Finding the Vertex The Axis of symmetry always goes through the _______. Thus, the Axis of symmetry gives us the ____________ of the vertex. STEP 1: Find the Axis of symmetry Vertex Find the vertex of y = -2x 2 + 8x - 3 a = -2 b = 8 X-coordinate The x- coordinate of the vertex is 2

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Finding the Vertex STEP 1: Find the Axis of symmetry STEP 2: Substitute the x – value into the original equation to find the y –coordinate of the vertex. The vertex is (2, 5) Find the vertex of y = -2x 2 + 8x - 3

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5 –1 STEP 3: Find two other points and reflect them across the Axis of symmetry. Then connect the five points with a smooth curve. 3 2 yx Graphing a Quadratic Function

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Y-intercept of a Quadratic Function Y-axis The y-intercept of a Quadratic function can Be found when x = 0. The constant term is always the y- intercept

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Example: Graph y= -.5(x+3) 2 +4 a is negative (a = -.5), so parabola opens down. Vertex is (h,k) or (-3,4) Axis of symmetry is the vertical line x = -3 Table of values x y -1 2 -2 3.5 -3 4 -4 3.5 -5 2 Vertex (-3,4) (-4,3.5) (-5,2) (-2,3.5) (-1,2) x=-3

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Your assignment:

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