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Today in Pre c alculus

In this lesson, we will go over the homework on quadratic functions and cover the topic of converting equations from standard form to vertex form. We will also discuss the formulas for finding the vertex of a parabola and practice using them. Homework exercises included.

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Today in Pre c alculus

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  1. Today in Precalculus • Go over homework • Notes: (no handout) • Quadratic Functions • Homework

  2. Quadratic Functions Standard form: f(x) = ax2 + bx + c Vertex form: f(x) = a (x – h)2 +k Vertex of the parabola (h, k) Axis of symmetry: x = h Roots (x-intercepts, zeros) found by factoring, quadratic formula or solving vertex form =0.

  3. Quadratic Functions To convert from standard form to vertex form using algebra: Complete the square. Example: y = 2x2 + 16x + 30 y = 2(x2 + 8x) + 30 Factor a only from x2 and x y = 2(x2 + 8x + 16)-32 + 30 Divide new b by 2 and square it, must also multiply by a and subtract to keep equation true. y = 2(x +4)2 – 2 Factor and simplify Parabola with vertex (-4, -2) and axis of symmetry x = -4. x – intercepts (-3,0), (-5,0)

  4. Practice Example: Use algebra to describe y = 3x2 – 18x – 3 y = 3(x2 – 6x) – 3 Factor a from x2 and x y = 3(x2 – 6x + 9) – 27 – 3 Divide new b by 2 and square it, must also multiply by a and subtract to keep equation true. y = 3(x – 3)2 – 30 Factor and simplify Parabola with vertex (3, -30) and axis of symmetry x = 3.

  5. Formulas for h and k Example: y = 2x2 + 16x + 31 k = 31 – (2)(-4)2 or k = 2(-4)2 +16(-4) + 31 k = -1 Vertex: (-4, -1)

  6. Practice Use the formulas to find the vertex of y = 3x2 + 5x – 4

  7. Example Write the equation for a parabola with a vertex (-1,2) that goes through (6,100). start with vertex form: y = a(x + 1)2 + 2 substitute point 100 = a(6 + 1)2 + 2 98 = 49a a = 2 y = 2(x + 1)2 + 2

  8. Homework • Pg. 182: 23-29odd (also find x-intercepts, may use your calculator), 35-41odd

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