# 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 = ax^{2} + 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 = 4x^{2} - 3x + 5

Therefore, the standard equation of the parabola is y = 4x^{2} - 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 = 4x^{2} - 3x + 5.

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