Identify the minimum value of the function y = 2x2 + 4x Answer
2 answers:
Answer:
y = - 2 is the minimum value
Step-by-step explanation:
The minimum value is the y- coordinate of the vertex.
The vertex lies on the axis of symmetry which is positioned at the midpoint of the zeros.
To find the zeros let y = 0, that is
2x² + 4x = 0 ← factor out 2x on the left side
2x(x + 2) = 0
Equate each factor to zero and solve for x
2x = 0 ⇒ x = 0
x + 2 = 0 ⇒ x = - 2
midpoint = = - 1 ← x- coordinate of vertex
Substitute x = - 1 into the equation for corresponding y- coordinate
y = 2(- 1)² + 4(- 1) = 2 - 4 = -2
vertex = (- 1, - 2)
Hence minimum value = - 2
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