Write an equation, in standard form, of a parabola that models the values in the table?
x | -1 | 0 | 2 |
f(x) | 12 | 5 | 15 |
Solution:
The equation of a parabola in standard form is given by:
y = ax2 + bx + c --- (1)
Put x = -1 and f(x) i.e. y = 12 in (1)
12 = a(-1)2 + b(-1) + c
12 = a - b + c --- (2)
Put x = 0 and f(x) i.e. y = 5 in (1)
5 = a(0)2 + b(0) + c
c = 5
Put x = 2 and f(x) i.e. y = 15 in (1)
15 = a(2)2 + b(2) + c
15 = 4a + 2b + c --- (3)
Put the value of c in (2) and (3),
(2) becomes 12 = a - b + 5
a - b = 12 - 5
a - b = 7 --- (4)
(3) becomes 15 = 4a + 2b + 5
4a + 2b = 15 - 5
4a + 2b = 10 --- (5)
On solving (4) and (5),
Multiply (4) by 2, 2a - 2b = 14 --- (6)
Adding (5) and (6), we get
6a = 24
a = 4
Put the value of a in (4)
4 - b = 7
-b = 7 - 4
b = -3
Substitute the values of a, b and c in (1)
y = 4x2 - 3x + 5
Therefore, the standard equation of the parabola is y = 4x2 - 3x + 5.
Write an equation, in standard form, of a parabola that models the values in the table?
Summary:
The equation, in standard form, of a parabola that models the values in the table is y = 4x2 - 3x + 5.
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