If the parabola ay^2+by+c=x passes through points (-4,17), (5,11), and (8,1) the value of a+b+c equals:?

Question

17/43; 5/2; 14/27; 8; -11

Answer 1

take the 3 points and substitute their values in the equation:

a(17)^2 + b(17) + c = -4
a(11)^2 + b(11) + c = 5
a(1)^2 + b(1) + c = 8

.

Answer 2

If the parabola ay²+by+c=x passes through points (-4,17), (5,11), and (8,1) the value of a+b+c equals:
17/43; 5/2; 14/27; 8; or -11

Since it passes through (8,1), when y = 1 x = 8

But when y = 1, ay²+by+c = a + b + c

Therefore a + b + c = 8

Answer 3

You have to solve 3 equations in 3 unknowns. The 3 unknowns are a, b, & c. The 3 equations are found by substituting the (x,y)coordinates of the 3 points for x and y in the equation:
a(17^2)+b(17)+c=-4
a(11^2)+b(11)+c=5
a(1^2)+b(1)+c=8 => a+b+c=8 (shortcut!)

Answer 4

Aha! I almost did this the REALLY hard way. Plug in the third point (8.1) to realise that a*1^2 + b*1 + c = 8
and that means a+b+c = 8