Answer:
n = -7,6
Step-by-step explanation:
n(n+1)+3=45
distributive property: a(b+c) = ab+ac
n²+n+3 = 45
n²+n -42 = 0
factor now
(n+7)(n-6) = 0
n = -7,6
Answer:
Step-by-step explanation:
Roots: set y = x^2 + 8x + 12 = 0 and solve for x: x + 6 = 0, so x = -6 is one root. The other is x = -2. The corresponding points are (-6, 0) and (-2, 0).
y-intercept: Let x = 0. Then y = 12. The y-intercept is (0, 12).
Axis of symmetry: x = -b / (2a) => x = -8/(2*1) = -4: x = -4
Vertex y-value: evaluate y at x = - 4: (-4)^2 + 8(-4) + 12 = -4: (-4, -4)
Arbitrarily chosen x value: x = 1 => 1^2 + 8(1) + 12 = 21: (1, 21)
The five points are: (-6, 0) and (-2, 0), (0, 12), (-4, -4), (1, 21). The vertex is (-4, -4). The parabolic graph opens UP.
So we know that:
3(-8 + 4v) = 8v
To find v, first simplify the left hand side:
-24 + 12v = 8v
Then group the "v's" over to the right:
-24 = -4v
-6 = -v
So v = 6
Hope this helped