# Unit #3: Quadratics 5-3: Translating Parabolas

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Unit #3: Quadratics 5-3: Translating Parabolas
Essential Question: How is the vertex form used in transforming a quadratic function?

5-3: Translating Parabolas
Yesterday, we explored quadratic equations in polynomial form: y = ax2 + bx + c Two other forms which are used are x-intercept (factored) form and vertex (transformation) form. Vertex form of a quadratic function is an equation in the form: y = a(x – h)2 + k Just like in polynomial form: If a is positive, the graph opens up If a is negative, the graph opens down

5-3: Translating Parabolas
y = a(x – h)2 + k The vertex is found at (h, k) h: Set what’s inside the parenthesis = 0 and solve for x k: Take the number that’s being added to the end of the function. Example Find the vertex of y = (x + 3)2 – 1 Because a = 1 (nothing in front of the parenthesis): The graph opens up. x + 3 = 0 → subtract 3 on each side → x = -3 h = -3, k = -1 The vertex is at (-3, -1).

5-3: Translating Parabolas
Determine the vertex of the quadratic function and whether the graph opens up or down. y = -3(x + 2)2 + 4 Opens: Vertex: y = 2(x – 2.5)2 – 5.5 y = -½(x – 2)2 Down (-2, 4) Up (2.5, -5.5) Down (2, 0)

5-3: Translating Parabolas
To find the y-intercept: Simply substitute “0” in for x and simplify Example: y = -2(x – 3)2 + 4 y = -2(0 – 3)2 + 4 = -2(-3) 2 + 4 = -2(9) + 4 = = -14 The y-intercept is at (0, -14)

5-3: Translating Parabolas
To convert into polynomial form: FOIL the parenthesis DISTRIBUTE (if necessary) the number outside COMBINE like terms Example: y = -2(x – 3)2 + 4 y = -2(x – 3)2 + 4 = -2(x – 3)(x – 3) + 4 = -2(x2 – 6x + 9) + 4 = -2x2 + 12x – y = -2x2 + 12x – 14

5-3: Translating Parabolas
Determine the y-intercept of the quadratic function and convert the function into polynomial form. y = -3(x + 2)2 + 4 y-intercept: Polynomial form: y = (x – 3)2 – 4 y = -½(x – 2)2 (0, -8) y = -3x2 – 12x – 8 (0, 5) y = x2 – 6x + 5 (0, -2) y = -½x2 + 2x – 2

5-3: Translating Parabolas
Assignment Page 251 Problems 1-11, odd Ignore the directions!!! Tell me: Whether the graph opens up or opens down The vertex The y-intercept The function written in polynomial form Note: You may want to do part (d) before part (c) Tomorrow, Practice with graphing Friday, Quiz on 5-1 through 5-3