Question

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Write the equation, in standard form, of the parabola containing the following points:
(0, 1), (1, 5), (2, 3)

Answer 1

f(x) = -3x² + 7x + 1

Explanation:

When parabola f(x) = ax² + bx + c passes through point (x₁, y₁) that means if x=x₁ then f(x)=f(x₁)=y₁

(0, 1) ⇒ 1=a·0²+b·0+c ⇒ c=1

f(x) = ax² + bx + 1

(1, 5) ⇒ 5 = a·1² + b·1 + 1

5 = a + b + 1

-b = a - 4

b = - a + 4

(2, 3) ⇒ 3 = a·2² + b·2 + 1

3 = 4a + 2b + 1

-2b = 4a - 2

b = - 2a + 1

- a + 4 = - 2a + 1

a = - 3

b = -(-3) + 4 = 7

So the equation:

f(x) = -3x² + 7x + 1