Question

Use quadratic regression to find the equation for the parabola going through these three points (-7,134)(-3, 10)(5,50)

Answer 1

Answer:

Step-by-step explanation:

y = ax² + bx + c

a( - 7)² + b( - 7) + c = 134 ⇔ 49a - 7b + c = 134 ......... (1)

a( - 3)² + b( - 3) + c = 10 ⇔ 9a - 3b + c = 10 ......... (2)

a(5)² + b(5) + c = 50 ⇔ 25a + 5b + c = 50 ......... (3)

(1) - (2)

40a - 4b = 124 ⇔ 10a - b = 31 ........... (4)

(3) - (2)

16a + 8b = 40 ⇔ 2a + b = 5 ........... (5)

(4) + (5)

12a = 36 ⇒ a = 3

2(3) + b = 5 ⇒ b = - 1

9(3) - 3( - 1) + c = 10 ⇒ c = - 20

y = 3x² - x - 20

y = [ 3 ] x² + [ - 1 ] x + [ - 20 ]