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VERTEX Form of Quadratic Functions

VERTEX Form of Quadratic Functions. Math 2Y. Vertex Form:. h moves the parabola horizontally k moves the parabola vertically a makes the parabola narrow or wide VERTEX => (opposite h , k ) Axis of Symmetry is x = opposite h *Reminder* If a > 0 (positive), parabola opens up

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VERTEX Form of Quadratic Functions

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  1. VERTEX Form of Quadratic Functions Math 2Y

  2. Vertex Form: • h moves the parabola horizontally • k moves the parabola vertically • a makes the parabola narrow or wide • VERTEX => (opposite h, k) • Axis of Symmetry is x = opposite h *Reminder* If a > 0 (positive), parabola opens up If a < 0 (negative), parabola opens down

  3. Identify the constants a = – , h = – 2, and k = 5. Because a < 0, the parabola opens down. 14 14 EXAMPLE 1 Graph a quadratic function in vertex form Graphy= – (x + 2)2 + 5. SOLUTION STEP 1 STEP 2 Plot the vertex (h, k) = (– 2, 5) and draw the axis of symmetry x = – 2.

  4. – – x = 0: y = (0 + 2)2 + 5 = 4 x = 2: y = (2 + 2)2 + 5 = 1 14 14 EXAMPLE 1 Graph a quadratic function in vertex form STEP 3 Evaluate the function for two values of x. Plot the points (0, 4) and (2, 1) and their reflections in the axis of symmetry. Draw a parabola through the plotted points. STEP 4

  5. GUIDED PRACTICE Graph the function. Label the vertex and axis of symmetry. 1. y = (x + 2)2 – 3 h = k = Vertex: ( ___ , ___ ) a = Axis of symmetry: x =

  6. GUIDED PRACTICE 2. y = –(x + 1)2 + 5 h = k = Vertex: ( ___ , ___ ) a = Axis of symmetry: x =

  7. 12 GUIDED PRACTICE 3. f(x)= (x – 3)2 – 4 h = k = Vertex: ( ___ , ___ ) a = Axis of symmetry: x =

  8. Writing in Standard Form • Goal is to manipulate the numbers so that they are in the form f(x) = ax² + bx + c *Reminder* Order of Operations: PEMDAS!! • You will need to distribute monomials, binomials, and trinomials! • Let’s look at some examples…

  9. EXAMPLE 3 Change from intercept form to standard form Write y = –2(x + 5)(x –8) in standard form. y = –2(x + 5)(x – 8) Write original function. = –2(x2 – 8x + 5x – 40) Multiply by Distributing. = –2(x2 – 3x – 40) Combine like terms. = –2x2 + 6x + 80 Distributive property

  10. EXAMPLE 3 Change from vertex form to standard form Write f (x) = 4(x – 1)2 + 9 in standard form. f (x) = 4(x – 1)2 + 9 Write original function. = 4(x – 1) (x – 1) + 9 Rewrite(x – 1)2. = 4(x2 – x – x + 1) + 9 Multiply by Distributing. = 4(x2 – 2x + 1) + 9 Combine like terms. = 4x2 – 8x + 4 + 9 Distributive property = 4x2 – 8x + 13 Combine like terms.

  11. GUIDED PRACTICE Write the quadratic function in standard form. 7. y = –(x – 2)(x – 7) ANSWER –x2 + 9x – 14 8. y = – 4(x – 1)(x + 3) ANSWER –4x2 – 8x + 12

  12. GUIDED PRACTICE Write the quadratic function in standard form. 9. y = –3(x + 5)2 –1 ANSWER –3x2 – 30x – 76 10. g(x)= 6(x – 4)2 –10 ANSWER 6x2 – 48x + 86

  13. GUIDED PRACTICE Graph the function. Label the vertex, axis of symmetry, and zeros. 4. y = (x – 3)(x – 7) Zeros: Vertex: ( ___ , ___ ) Axis of symmetry: x =

  14. GUIDED PRACTICE 5. f (x) = 2(x – 4)(x + 1) Zeros: Vertex: ( ___ , ___ ) Axis of symmetry: x =

  15. Assignment => Textbook pg. 67 # 2-14 even, 20, 22, 28, 30 (You will be given 6 blank graphs for #12, 14, 20, 22)

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