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Daily Check

Daily Check. Factor: 3x 2 + 10x + 8 Factor and Solve: 2x 2 - 7x + 3 = 0. Math I. UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you graph quadratic functions in vertex form? Standard: MM2A3.b.

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Daily Check

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  1. Daily Check • Factor: 3x2 + 10x + 8 • Factor and Solve: 2x2 - 7x + 3 = 0

  2. Math I UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do you graph quadratic functions in vertex form? Standard: MM2A3.b.

  3. 3.2 Graphing Quadratic Functions in Vertex or Intercept Form • Definitions • 3 Forms • Steps for graphing each form • Examples • Changing between eqn. forms

  4. Quadratic Function • A function of the form y=ax2+bx+c where a≠0 making a u-shaped graph called a parabola. Example quadratic equation:

  5. Vertex- • The lowest or highest point of a parabola. Vertex Axis of symmetry- • The vertical line through the vertex of the parabola. Axis of Symmetry

  6. Vertex Form Equation y=a(x-h)2+k • If a is positive, parabola opens up If a is negative, parabola opens down. • The vertex is the point (h,k). • The axis of symmetry is the vertical line x=h. • Don’t forget about 2 points on either side of the vertex! (5 points total!)

  7. Vertex Form • Each function we just looked at can be written in the form (x – h)2 + k, where (h , k) is the vertex of the parabola, and x = h is its axis of symmetry. • (x – h)2 + k – vertex form

  8. Example 1: Graph y = (x + 2)2 + 1 • Analyze y = (x + 2)2 + 1. • Step 1 Plot the vertex (-2 , 1) • Step 2 Draw the axis of symmetry, x = -2. • Step 3 Find and plot two points on one side , such as (-1, 2) and (0 , 5). • Step 4 Use symmetry to complete the graph, or find two points on the • left side of the vertex.

  9. Your Turn! • Analyze and Graph: y = (x + 4)2 - 3. (-4,-3)

  10. Example 2: Graphy= -.5(x+3)2+4 • a is negative (a = -.5), so parabola opens down. • Vertex is (h,k) or (-3,4) • Axis of symmetry is the vertical line x = -3 • Table of values x y -1 2 -2 3.5 -3 4 -4 3.5 -5 2 Vertex (-3,4) (-4,3.5) (-2,3.5) (-5,2) (-1,2) x=-3

  11. Now you try one! y=2(x-1)2+3 • Open up or down? • Vertex? • Axis of symmetry? • Table of values with 4 points (other than the vertex?

  12. (-1, 11) (3,11) X = 1 (0,5) (2,5) (1,3)

  13. Intercept Form Equation y=a(x-p)(x-q) • The x-intercepts are the points (p,0) and (q,0). • The axis of symmetry is the vertical line x= • The x-coordinate of the vertex is • To find the y-coordinate of the vertex, plug the x-coord. into the equation and solve for y. • If a is positive, parabola opens up If a is negative, parabola opens down.

  14. Example 3: Graph y=-(x+2)(x-4) • The axis of symmetry is the vertical line x=1 (from the x-coord. of the vertex) • Since a is negative, parabola opens down. • The x-intercepts are (-2,0) and (4,0) • To find the x-coord. of the vertex, use • To find the y-coord., plug 1 in for x. • Vertex (1,9) (1,9) (-2,0) (4,0) x=1

  15. Now you try one! y=2(x-3)(x+1) • Open up or down? • X-intercepts? • Vertex? • Axis of symmetry?

  16. x=1 (-1,0) (3,0) (1,-8)

  17. Changing from vertex or intercepts form to standard form • The key is to FOIL! (first, outside, inside, last) • Ex: y=-(x+4)(x-9) Ex: y=3(x-1)2+8 =-(x2-9x+4x-36) =3(x-1)(x-1)+8 =-(x2-5x-36) =3(x2-x-x+1)+8 y=-x2+5x+36 =3(x2-2x+1)+8 =3x2-6x+3+8 y=3x2-6x+11

  18. Challenge Problem • Write the equation of the graph in vertex form.

  19. Assignment Day 1 -p. 65 #4,6,7,9,13,16 and Review for Quiz Day 2 – p. 67 #4,5,7,9,11-14 We will not do intercept form.

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