Answer:
V: (4, -2), min, Axis: x = 4, Roots 2 and 6
Step-by-step explanation:
Multiply everything x 2 to get rid of the decimal in front of x^2
2y = x^2 - 8x + 12
Factor
2y = (x - 6)(x - 2)
The roots are at 2 and 6.
The axis of symmetry is in the center between the roots, so it is x = 4.
Put 4 into the original equation to find y
y = 0.5(4*2) - 4(4) + 6
y = 8 - 16 + 6, y = -2
Vertex is at (4, -2). It is a minimum because the graph opens up since x*2 is positive.
Answer:
C₂₃ = -186
↓
C₁₃ = -32
↓
C₃₁ = 6
↓
C₁₁ = 27
↓
C₂₁ = 28
↓
C₃₃ = 38
↓
C₂₂ = 56
↓
C₃₂ = 90
↓
C₁₂ = 115
Step-by-step explanation:
The given matrices are;
The cross product of the matrices is found as follows;
C₁₁ = 1×5 + 7×3 + (-1) × (-1) = 27
C₁₂ = 1×1 + 7×15 + (-1)×(-9) = 115
C₁₃ = 1×7 + 7×(-2) + (-1)×25 = -32
C₂₁ = 5×5 + (-2)×3 + (-9) × (-1) = 28
C₂₂ = 5×1 + (-2)×15 + (-9)×(-9) = 56
C₂₃ = 5×7 + (-2)×(-2) + (-9)×25 = -186
C₃₁ = (-3)×5 + 8×3 + 3 × (-1) = 6
C₃₂ = (-3)×1 + 8×15 + 3×(-9) = 90
C₃₃ = (-3)×7 + 8×(-2) + 3×25 = 38
Therefore, we get;
In increasing order, we have;
C₂₃ = -186
↓
C₁₃ = -32
↓
C₃₁ = 6
↓
C₁₁ = 27
↓
C₂₁ = 28
↓
C₃₃ = 38
↓
C₂₂ = 56
↓
C₃₂ = 90
↓
C₁₂ = 115