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Warm-up

Warm-up. Error Analysis: Look at the following problem. Determine if the vertex is accurate. Graph the parabola correctly and label the vertex and axis of symmetry. y = (x – 2) 2 + 4 Vertex = (2, -4). Steps: Standard Vertex . Find the vertex

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Warm-up

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  1. Warm-up Error Analysis: Look at the following problem. Determine if the vertex is accurate. Graph the parabola correctly and label the vertex and axis of symmetry. y = (x – 2)2 + 4 Vertex = (2, -4)

  2. Steps: Standard Vertex Find the vertex It’s in standard form, so use –b/2a to find x, then plug that in to find y. So the vertex is (h,k) Now write the general vertex form. Y = a(x – h)2 + k The “a” in front of the vertex form is the same as it was in the standard form equation.

  3. Ex1. Write the function y = 2x2 + 10x + 7 in vertex form. x-coordinate: -b/2a -10/2(2) = -10/4 =-5/2 or - 2.5 y-coordinate: 2(-2.5)2 + 10(-2.5) + 7 -5.5 Substitute the vertex point (-2.5,-5.5) into the vertex form y = a(x – h)2 + k a from above y = 2(x + 2.5)2 – 5.5

  4. Ex2. Write y = -3x2 +12x + 5 in vertex form. x-intercept: -b/2a = -12/2(-3) = -12/-6 = 2 y-intercept: y = -3(2)2 + 12(2) + 5 = 17 Re-write in vertex form: y = -3(x – 2)2 + 17

  5. Write in vertex form:

  6. Write in vertex form:

  7. Write in vertex form:

  8. Write in vertex form:

  9. From vertex to standard form: To change an equation from vertex to standard form, you have to multiply out the function. y = 3(x -1)2 + 12 y = 3(x – 1)(x – 1) + 12 y = 3(x2 – 2x + 1) + 12 y = 3x2 – 6x + 3 + 12 y = 3x2 – 6x + 15

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