1 / 15

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

wlew
Download Presentation

VERTEX Form of Quadratic Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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)

More Related