A parabola \(ax^2+bx+c\) contains the points (-1,0) , (0,5) , and (5,0) . Find the value 100a+10b+c .
A parabola contains the points (-1,0) , (0,5) , and (5,0) . Find the value 100a+10b+c .
It's obvious that c = 5
So
a(-1)^2 + b(-1) + 5 = 0 → a - b + 5 = 0 → a - b = -5 → a + 5 = b (1)
And
a(5)^2 + b(5) + 5 = 0 → 25a + 5b = -5 → 5a + b = -1 (2)
Sub (1) into (2)
5a + (a + 5) = -1
6a + 5 = -1 subtract 5 from both sides
6a = -6
a = -1 and a + 5 = b ....so...... -1 + 5 = b = 4
So our function is
y = -1x^2 + 4x + 5
So
100a + 10b + c =
100 (-1) + 10 (4) + 5 =
-100 + 40 + 5 =
-100 + 45 =
-55