Graphing Quadratic Functions In Vertex Form Definitions 2

Graphing Quadratic Functions In Vertex Form • Definitions • 2 more forms for a quad. function • Steps for graphing Vertex Form • Examples

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!)

Example 2: Graph y=-½(x+3)2+4 y=a(x-h)2+k • • a is negative (a = -½), 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 Vertex (-3, 4) -2 3. 5 (-4, 3. 5) (-2, 3. 5) -3 4 -4 3. 5 (-5, 2) (-1, 2) -5 2 x=-3

Now you try one! y=a(x-h)2+k y=2(x-1)2+3 • Open up or down? • Vertex? • Axis of symmetry? • Table of values with 5 points?

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

Civil Engineering The Tacoma Narrows Bridge in Washington has two towers that each rise 307 feet above the roadway and are connected by suspension cables as shown. Each cable can be modeled by the function. y= 1 (x – 1400)2 + 27 7000 where x and y are measured in feet. What is the distance d between the two towers ?

SOLUTION The vertex of the parabola is (1400, 27). So, a cable’s lowest point is 1400 feet from the left tower shown above. Because the heights of the two towers are the same, the symmetry of the parabola implies that the vertex is also 1400 feet from the right tower. So, the distance between the two towers is d = 2 (1400) = 2800 feet.