Question

Use the provided information to write the standard form equation of the parabola.

Opens up or down, and passes through (4,-5), (0,3), and (-1,10)

Answer 1

f(x) = x² - 6x + 3

Explanation:

Parabola f(x) = ax² + bx + c passing through point (x₁, y₁) means if x=x₁ then f(x)=f(x₁)=y₁

(0, 3) ⇒ 3=a·0²+b·0+c ⇒ c=3

f(x) = ax² + bx + 3

(4, -5) ⇒ -5 = a·4² + b·4 + 3

-5 = 16a + 4b + 3

-4b = 16a + 8

b = - 4a - 2

(-1, 10) ⇒ 10 = a·(-1)² + b·(-1) + 3

10 = a - b + 3

b = a - 7

a - 7 = - 4a - 2

5a = 5

a = 1

b = 1 - 7 = - 6

So the equation:

f(x) = x² - 6x + 3