A strip shape determining apparatus for a rolled metal strip , the strip shape determining apparatus comprising: a camera that is installed so as to capture an image including an area where band shaped reflection light that crosses a surface of the rolled metal strip in a strip width direction is visible; and an image processing unit that determines a strip shape of the metal strip on a basis of the image captured by the camera , the image processing unit dividing the area within the image into a plurality of segments in the strip width direction of the metal strip , converting a position in the strip width direction within a strip width range of the area within the image into a range of -1 ≤ x ≤ 1 supposing that a value indicating a strip width direction position of each of the segments formed by the division is a variable (x), and obtaining coefficients (C 0 ', C 1 ', C 2 ', and C 4 ') of a Chebyshev polynomial of a following Equation by applying index information indicating a size of the area in each segment formed by the division to the Chebyshev polynomial including only a zeroth order term, a first order term, a second order term, and a fourth order term of x, the Chebyshev polynomial having the index information as a distribution E(x) of each of the segments, and transferring, as a determination result signal of a strip elongation distribution in the strip width direction, one or more of the coefficients including a zeroth order coefficient (C 0 '), a first order coefficient (C 1 '), a second order coefficient (C 2 '), and a fourth order coefficient (C 4 ') as information corresponding to the distribution in the strip width direction of strip elongation in a rolling direction. E x = C 0 ′ + C 1 ′ × x + C 2 ′ × 2 x 2 − 1 + C 4 ′ × 8 x 4 − 8 x 2 + 1 where − 1 ≤ x ≤ 1 a camera that is installed so as to capture an image including an area where band shaped reflection light that crosses a surface of the rolled metal strip in a strip width direction is visible; and an image processing unit that determines a strip shape of the metal strip on a basis of the image captured by the camera , the image processing unit dividing the area within the image into a plurality of segments in the strip width direction of the metal strip , converting a position in the strip width direction within a strip width range of the area within the image into a range of -1 ≤ x ≤ 1 supposing that a value indicating a strip width direction position of each of the segments formed by the division is a variable (x), and obtaining coefficients (C 0 ', C 1 ', C 2 ', and C 4 ') of a Chebyshev polynomial of a following Equation by applying index information indicating a size of the area in each segment formed by the division to the Chebyshev polynomial including only a zeroth order term, a first order term, a second order term, and a fourth order term of x, the Chebyshev polynomial having the index information as a distribution E(x) of each of the segments, and transferring, as a determination result signal of a strip elongation distribution in the strip width direction, one or more of the coefficients including a zeroth order coefficient (C 0 '), a first order coefficient (C 1 '), a second order coefficient (C 2 '), and a fourth order coefficient (C 4 ') as information corresponding to the distribution in the strip width direction of strip elongation in a rolling direction. E x = C 0 ′ + C 1 ′ × x + C 2 ′ × 2 x 2 − 1 + C 4 ′ × 8 x 4 − 8 x 2 + 1 where − 1 ≤ x ≤ 1 <EOS>