Quadratic Functions Sketching the graph of Quadratic Functions

Remember… y = a(x – p) 2 + q is called vertex-graphing form a  determines direction of opening p and q  determine coordinates of vertex x = p  equation for axis of symmetry

Sketching the Graph Example 1: Sketch the graph of the quadratic function f(x) = -2(x-3) by: a) determining the vertex b) the y-intercept c) the reflection of the y-intercept about the axis of symmetry

Sketching the Graph Solution to a):f(x) = -2(x-3)2 + 8 By looking at the function, we can determine that p = 3 and q = 8. Therefore, the coordinates of the vertex are (3,8). (3, 8) x = p Graph the vertex (3, 8) and draw the axis of symmetry x = 3.

Sketching the Graph (3, 8) Solution to b): f(x) = -2(x-3)2 + 8 To find y- intercept, set x = 0. y = -2(0 – 3) y = -2(-3) y = -2(9) + 8 y = y = -10 (0, -10)

Sketching the Graph Solution to c): f(x) = -2(x-3)2 + 8 (3, 8) (0, -10) Notice that (0, -10) is 3 units to the left of the axis of symmetry. Thus, the point (6, -10) which is 3 units to the right, must also be on the parabola curve. (6, -10) 3 units to the left 3 units to the right

Sketching the Graph Example 2: Find the x-intercepts of the quadratic function f(x) -3(x + 1) Sketch the graph using the x-intercepts and the vertex. Solution: To find the x-intercepts, set f(x) = 0. 0 = -3(x + 1) (x + 1) 2 = 27 (x + 1) 2 = 9 x + 1 = x + 1 = ± 3 x = -1 ± 3  x = 2orx = -4  Divide both sides by 3  Take the square root of both sides

Sketching the Graph With x-intercepts of (2, 0) and (-4, 0), and determine the vertex to be (-1, 27) we can sketch the graph. (-1, 27) (-4, 0)(2, 0)

Homework Do #3 a,c,e,g and #4 a,c for tomorrow