Lesson #4: Quadratic Relations May 16, 2011

Quadratic Relations produce curves that we call PARABOLAS Quadratic Relations produce curves that we call PARABOLAS. Parabolas are U shaped and they can look like a right-side up U or an up-side down U. As with linear relations, quadratic relations can be identified by key components and characteristics. These are:

All quadratics can be written/expressed in standard form: Equations All quadratics can be written/expressed in standard form: where c is constant. The key feature is that one of the x values has an exponent of 2.

EX: a) b) c)

2. Graphs When graphed, quadratic relations will form a smooth curve. (This is called a parabola). Once again, the parabola can open upward, or downward and can be skinny or fat. The curve will be symmetrical, and we call the line directly in the middle of the curve the AXIS OF SYMMETRY.

AXIS OF SYMMETRY is also written as x = (x coordinate of the vertex) EX:

3.Table of Values All quadratic relations have second differences that are equal (or constant). Second differences are the difference in value between consecutive first differences. EX: Find the second differences. Does the table display a quadratic relation? X 1 2 3 4 5 6 Y 17 7 -1 First differences: 10, 6, 2, -2, -6, -10 Second Differences: 4, 4, 4, 4, 4

Hand in Page 304 # 5 (correct the statement if false), 7 x y -3 20 -2 8 -1 2 1 3 38 First Differences: 12, 6, 0, -6, -12, -18 Second Differences: 6, 6, 6 ,6, 6 Complete Page 303 # 1-4, 6 Hand in Page 304 # 5 (correct the statement if false), 7