The pose of the quadratic business office graph seen from the publish of intercepts amongst the 10 axis, is determined past times the discriminant value of D = b2 - 4ac. While the nautical chart opens upward or downwardly is determined past times the sign a (coefficient x2).
Here are around possible nautical chart positions seen from discriminants too signs (coefficient x2)):
Information :
a. At (a) too (e) for D > 0 the graph intersects the 10 axis at ii points, if a > 0 graph opens upward instead opens downward when a < 0.
b. At (b) too (f) for D = 0 the graph cuts off at i indicate or offends the 10 axis.
c. In (c) too (g) the graph does non intersect the 10 axis
For a > 0 too D < 0 all graphs to a higher house the 10 axis hateful all business office values are positive for all prices 10 too this is normally called positive definite.
For a < 0 too D > 0 all the charts below the 10 axis hateful that the whole map or business office value is negative for all the cost of 10 too commonly called the negative definite.
Example:
Without drawing a graph, delight decide the properties of the quadratic business office f(x) = x2 - 3x - four !
Answer :
f(x) = x2 - 3x - 4
y = x2 - 3x - 4
a = 1
b = -3
c = -4
a = 1 agency a > 0 (a positive), too thus the graph must opened upward up
D = b2 - 4ac = (-3)2 -4(1)(-4) = nine + xvi = 25
Because D > 0 (D positive), too thus the graph intersects the 10 axis at ii dissimilar points. So the business office graph of f is a parabola that opens upward too cuts 10 axis at ii dissimilar points (a > 0 too D > 0)
Similarly this article.
Sorry if at that spot is a incorrect word.
The halt of discussion wassalamualaikum wr. wb
Referensi :
- To'Ali's majority math grouping accounting too sales