Respuesta :
Based on the information given, the required equation of parabola will be y= -3x² - 14x + 12.
Solution
The parabola passes through the points (-1, 23), (1, -5), (3, -57). Let the equation of the parabola be y = ax² + bx + c.
For point (-1, 23), this will be:
23 = a(-1)² + b(-1) + c
23 = a - b + c ..... equation i
For point (1, -5), this will be:
-5 = a(1)² + b(1) + c
-5 = a + b + c .... equation ii
For point (3, -57), this will be:
-57 = a(3)² + b(3) + c
-57 = 9a + 3b + c .... equation iii
From equation i, 23 = a - b + c
Therefore, c = 23 - a + b .... equation iv
Substitute c into equation ii
-5 = a + b + 23 - a + b
-5 = 2b + 23
2b = -23 - 5.
2b = -28
b = -28/2 = -14
Substitute c into equation iii
-57 = 9a + 3b + 23 - a + b
-80 = 8a + 4b.
-80 = 8a + 4(-14)
-80 = 8a - 56
8a = -80 + 56
8a = -24
a = -24/8 = -3
Therefore, the value of c will be:
c = 23 - a + b
c = 23 -(-3) + (-14)
c = 23 + 3 - 14
c = 12
In conclusion, the required equation of parabola will be y = -3x² - 14x + 12.
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