The graph cuts the x-axis at (x1, 0) and (x2, 0) through any point (x3, y3) on the graph, then the equation is y = a (x - x1) (x - x2)
The graph has a turning point p (xp, yp) seta through any point (x1, y1) on the graph, then the equation is y = a (x - xp)2 + yp
The graphs through the three points (x1, y1), (x2, y2), (x3, y3), then the equation is y = ax2 + bx + c
Example :
Please determine the graphic equations of the graph functions below!
Answer :
The graph intersects the x-axis at points (-2, 0) and (3, 0)
Thus y = a (x + 2) (x - 3) through the point (1, 6)
6 = a(1 + 2)(1 - 3)
6 = a(3)(-2)
6 = -6a
6/-6 = -6a/-6
-1 = a
Substituting again a = -1 to y = a(x + 2) (x - 3) is obtained:
y = a(x + 2)(x - 3)
y = -1(x + 2)(x - 3)
y = -1(x2 - 3x + 2x - 6)
y = -1(x2 - x - 6)
y = -x2 + x + 6
So the function graph equation is y = -x2 + x + 6.
Similarly this article.
Sorry if there is a wrong word.
The end of word wassalamualaikum wr. wb
Referensi :
- To'Ali's book math group accounting and sales
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