Quadratic Functions Graph Position

The position of the quadratic function graph seen from the number of intercepts with the x axis, is determined by the discriminant value of  D = b² - 4ac. While the chart opens up or down is determined by the sign a (coefficient x²).

Here are some possible chart positions seen from discriminants and signs (coefficient x²)):

Information :
a. At (a) and (e) for D > 0 the graph intersects the x axis at two points, if a > 0 graph opens upward instead opens downward when a < 0.

b. At (b) and (f) for D = 0 the graph cuts off at one point or offends the x axis.

c. In (c) and (g) the graph does not intersect the x axis
For a > 0 and D < 0 all graphs above the x axis mean all function values are positive for all prices x and this is usually called positive definite.
For a < 0 and D > 0 all the charts below the x axis mean that the whole map or function value is negative for all the price of x and commonly called the negative definite.

Example:
Without drawing a graph, please determine the properties of the quadratic function f(x) = x² - 3x - 4 !

Answer :
f(x) = x² - 3x - 4
y = x² - 3x - 4

a = 1
b = -3
c = -4

a = 1 means a > 0 (a positive), then the graph must open up

D = b² - 4ac = (-3)² -4(1)(-4) = 9 + 16 = 25
Because D > 0 (D positive), then the graph intersects the x axis at two different points. So the function graph of f is a parabola that opens up and cuts x axis at two different points (a > 0 and D > 0)

Similarly this article.
Sorry if there is a wrong word.
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Referensi :

• To'Ali's book math group accounting and sales

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