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Factor and Solve Quadratic Equations Ms. Nong What is in this unit? Graphing the Quadratic Equation  Identify the vertex and intercept(s) for a parabola.

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Presentation on theme: "Factor and Solve Quadratic Equations Ms. Nong What is in this unit? Graphing the Quadratic Equation  Identify the vertex and intercept(s) for a parabola."— Presentation transcript:

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2 Factor and Solve Quadratic Equations Ms. Nong

3 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

4 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

5 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.

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

7 All parts labeled

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

9 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

10 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

11 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

12 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

13 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

14 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

15 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 Vertex (-3,4) (-4,3.5) (-5,2) (-2,3.5) (-1,2) x=-3

16 Your assignment:


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